Qualitative risk analysis methods

After all have been identified possible risks for a specific project, it is necessary to determine the feasibility of investments, development and work on this project. To do this, an analysis of the risks of the investment project is carried out.

All possible risk analysis methods proposed in theory can be divided into qualitative and quantitative approaches. A qualitative approach, in addition to identifying risks, involves identifying the sources and causes of their occurrence, as well as a cost assessment of the consequences. The main features of the qualitative approach are: identifying simple risks for the project, identifying dependent and independent risks both from each other and from external factors, and determining whether the risks are removable or not.

With the help of qualitative analysis, all risk factors are determined that entail, to one degree or another, losses or losses of the enterprise, as well as the likelihood and time of their occurrence. For the worst-case scenario for the development of the project, the maximum amount of losses for the company is calculated.

In the qualitative approach, the following methods of risk analysis are distinguished: the method of expert assessments; cost feasibility method; method of analogies.

Method of expert assessments.

The expert assessment method includes three main components. Firstly, an intuitive-logical analysis of a problem is based only on the intuitive assumptions of certain experts; only their knowledge and experience can serve as a guarantor of the correctness and objectivity of the conclusions. Secondly, issuing expert assessment decisions; this stage is the final part of the expert’s work. Experts formulate a decision on the advisability of working with the project they are researching, and offer an assessment of the expected results under different scenarios for the development of the project. The third stage, the final one for the expert assessment method, is the processing of all decision results. In order to obtain a final assessment, all received assessments from experts must be processed, and an overall relatively objective assessment and decision regarding a particular project must be identified.

Experts are asked to fill out a questionnaire with a detailed list of risks related to the project being analyzed, in which they need to determine the likelihood of the risks they have identified on a certain scale. The most common methods of expert risk assessments include the Delphi method, scoring method, ranking, pairwise comparison, and others.

The Delphi method is one of the expert assessment methods that provides quick search decisions, among which the best solution is subsequently selected. The use of this method allows you to avoid contradictions among experts and obtain independent individual decisions, eliminating communication between experts during the survey. The experts are given a questionnaire, to the questions of which they must give independent, as objective as possible assessments, and reasonable assessments. Based on the completed questionnaires, the decision of each expert is analyzed, the prevailing opinion, extreme judgments are identified, decisions are as clearly, accessible and well-reasoned as possible, etc. Subsequently, experts may change their opinion. The entire operation is usually carried out in 2-3 rounds, until the opinions of experts begin to coincide, which will be the final result of the study.

The risk scoring method is based on a general indicator determined by a number of private expert-assessed risk indicators. It consists of the following steps:

• 1) Determination of factors that influence the occurrence of risk;
• 2) Selection of a general indicator and a set of specific criteria characterizing the degree of risk for each factor;
• 3) Drawing up a system of weighting coefficients and rating scales for each indicator (factor);
• 4) Integral assessment of the generalized criterion for the degree of project risks;
• 5) Development of recommendations for risk management.

The ranking method involves arranging objects in ascending or descending order of some inherent property. Ranking allows you to select the most significant factor from the set of factors being studied. The result of the ranking is the ranking.

If available n objects, then as a result of their ranking by the j-th expert, each object receives a score x ij - the rank assigned to the i-th object by the j-th expert. The values ​​of x ij are in the range from 1 to n. The rank of the most important factor is equal to one, the least significant - to the number n. The ranking of the jth expert is the sequence of ranks x 1j , x 2j , …, x nj .

This method is simple to implement, but when assessing a large number of parameters, experts are faced with the difficulty of constructing a ranked series, due to the fact that it is necessary to simultaneously take into account many complex correlations.

The pairwise comparison method is the establishment of the most preferred objects when comparing all possible pairs. In this case, there is no need, as in the ranking method, to order all objects; it is necessary to identify a more significant object in each of the pairs or establish their equality.

Again, in comparison with the ranking method, pairwise comparison can be carried out with a large number of parameters, as well as in cases of slight differences in parameters (when it is practically impossible to rank them, and they are combined into a single one).

When using the method, a matrix of size is most often compiled nxn, Where n- number of compared objects. When comparing objects, the matrix is ​​filled with elements a ij as follows (another filling scheme can be proposed):

The sum (per line) in this case allows you to assess the relative importance of objects. The object for which the amount is the largest can be considered the most important (significant).

Summation can also be done by columns (), then the most significant factor will be the one with the fewest points.

Expert analysis consists of determining the degree of risk influence based on expert assessments of specialists. The main advantage of this method is the simplicity of calculations. There is no need to collect accurate source data and use expensive and software. However, the level of risks depends on the knowledge of experts. Another disadvantage is the difficulty in attracting independent experts and the subjectivity of their assessments. For clarity and objectivity of the results, this method can be used in conjunction with other quantitative methods (more objective).

Method of relevance and expediency of costs, method of analogies.

A cost-benefit analysis is based on assumptions that certain factors (or one of them) are causing the project to overspend. These factors include:

• · initial underestimation of the cost of the project as a whole or its individual phases and components;
• · changes in design boundaries due to unforeseen circumstances;
• · differences in the performance of machines and mechanisms from those envisaged by the project;
• · an increase in the cost of the project compared to the original, due to inflation or change tax legislation.

To carry out the analysis, first of all, all the above factors are detailed, then a tentative list of possible increases in project costs is compiled for each option for its development. The entire process of project implementation is divided into stages, based on this, the process of financing for the development and implementation of the project is also divided into stages. However, the funding stages are set conditionally, as some changes may be made as the project develops and develops. Phased investment of funds allows the investor to more carefully monitor the work on the project, and if risks increase, either terminate or suspend financing, or begin to take certain measures to reduce costs.

Among qualitative methods risk analysis, the method of analogies is also common. The main idea of ​​this method is to analyze other projects similar to the one being developed. Based on the same risky projects, possible risks, the reasons for their occurrence, the consequences of the risks are analyzed, and the consequences of the impact of unfavorable external or internal factors on the project are studied. The received information is then projected onto new project, which allows you to identify all the maximum possible potential risks. The source of information can be the reliability ratings of design, contracting, investment and other companies regularly published by Western insurance companies, analyzes of trends in demand for specific products, prices for raw materials, fuel, land, etc. .

The difficulty of this method of analysis is the difficulty of obtaining the most accurate analogue, due to the fact that there are no formal criteria that precisely establish the degree of similarity of situations. But, as a rule, even if the analogue is selected correctly, it becomes difficult to formulate the correct prerequisites for analysis, a complete and close to reality set of scenarios for project failure. The reason is that there are very few completely identical projects or none at all; any project under study has its own individual characteristics and risks, which are interconnected according to the uniqueness of the project, so it is not always possible to absolutely accurately determine the cause of a particular risk.

A brief description of the cost moderation method and the method of analogies indicates that they are more suitable for identifying and describing possible risk situations for a particular project than for obtaining even a relatively accurate assessment of the risks of an investment project.

Quantitative risk analysis method

To assess the risks of investment projects, the most common quantitative methods of analysis are:

• sensitivity analysis
• · script method
• · simulation modeling (Monte Carlo method)
• · discount rate adjustment method
• decision tree

Sensitivity Analysis

In the sensitivity analysis method, the risk factor is taken as the degree of sensitivity of the resulting indicators of the analyzed project to changes in the external or internal conditions of its functioning. The resulting project indicators are usually performance indicators (NPV, IRR, PI, PP) or annual project indicators (net profit, accumulated profit). Sensitivity analysis is divided into several successive stages:

• · the basic values ​​of the resulting indicators are established, the connection between the initial data and the resulting ones is mathematically established
• · the most probable values ​​of the initial indicators are calculated, as well as the range of their changes (usually within 5-10%)
• · the most probable values ​​of the resulting indicators are determined (calculated)
• · The original parameters under study are recalculated one by one within the obtained range, new values ​​of the resulting parameters are obtained
• · Initial parameters are ranked according to their degree of influence on the resulting parameters. Thus, they are grouped based on the degree of risk.

The degree of exposure of an investment project to the corresponding risk and the sensitivity of the project to each factor is determined by calculating the elasticity indicator, which is the ratio of the percentage change in the resulting indicator to a change in the value of the parameter by one percent.

Where: E - elasticity index

NPV 1 - the value of the basic resulting indicator

NPV 2 - the value of the resulting indicator when changing the parameter

X 1 - basic value of the variable parameter

X 2 - changed value of the variable parameter

The higher the elasticity index, the more sensitive the project is to changes in this factor, and the more susceptible the project is to the corresponding risk.

Also, sensitivity analysis can be carried out graphically, by plotting the dependence of the resulting indicator on changes in the factor under study. The sensitivity of the NPV value to a change in the factor changes the level of the slope of the relationship; the larger the angle, the more sensitive the values, and also the greater the risk. At the point of intersection of the direct response with the x-axis, the value of the parameter is determined in percentage terms at which the project will become ineffective.

After this, based on the calculations carried out, all the obtained parameters are ranked by degree of significance (high, medium, low), and a “sensitivity matrix” is constructed, with the help of which the factors that are the most and least risky for the investment project are identified.

Regardless of the inherent advantages of the method - objectivity and clarity of the results obtained, there are also significant disadvantages - changes in one factor are considered in isolation, whereas in practice all economic forces are correlated to one degree or another.

Scripting method

The scenario method represents a description of all possible conditions for project implementation (either in the form of scenarios or in the form of a system of restrictions on the values ​​of the main parameters of the project) as well as a description of possible results and performance indicators. This method, like all others, also consists of certain sequential steps:

• · at least three are being built possible options scenarios: pessimistic, optimistic, realistic (or most likely or average)
• · initial information about uncertainty factors is converted into information about the likelihood of individual implementation conditions and certain performance indicators

Based on the data obtained, the indicator is determined economic efficiency project. If the probabilities of the occurrence of a particular event reflected in the scenario are known exactly, then the expected integral effect of the project is calculated using the mathematical expectation formula:

Where: NPVi - integral effect when implementing the i-th scenario

pi is the probability of this scenario

In this case, the risk of project ineffectiveness (Re) is assessed as the total probability of those scenarios (k) in which the expected effectiveness of the project (NPV) becomes negative:

The average damage from the implementation of the project in case of its ineffectiveness (Ue) is determined by the formula:

The main disadvantage of the scenario analysis method is the factor of taking into account only a few possible outcomes for an investment project, but in practice the number of possible outcomes is not limited.

PERT analysis method (Program Evaluation and Review Technique)

Experts highlight the PERT analysis method (Program Evaluation and Review Technique) as one of the methods of scenario analysis. The main idea of ​​this method is that when developing a project, three project parameters are set - optimistic, pessimistic, most probable. Next, the expected values ​​are calculated using the following formula:

Expected value = [Optimistic value 4xMost likely value + Pessimistic value]/6

Coefficients 4 and 6 were obtained empirically based on statistical data from a large number of projects. Based on the calculation results, the rest of the project analysis is carried out. The effectiveness of PERT analysis is maximum only if the values ​​of all three estimates can be justified.

Decision tree

The decision tree method represents network graphs in which each branch represents various alternative options for the development of the project. By following each constructed branch of the project, you can trace all possible stages of the project’s development, and, accordingly, choose the most optimal one, and with the least risks. This analysis method is divided into the following stages:

• · Peaks are identified for each problematic and ambiguous moment in the development of the project, and branches are built (possible paths for the development of events)
• · For each arc, the probability and possible losses at this stage are determined by an expert method.
• · Based on all the obtained values ​​of the vertices, the most probable value of NPV (or other indicator significant for the project) is calculated
• · Probability distribution analysis is carried out

The only limitation and possible disadvantage of the method is the mandatory presence of a reasonable number of project development options. The main difference is the ability to take full and detailed account of all factors and risks affecting the project. The method is especially used in situations where decisions on project implementation are made gradually, and depend on previously made decisions, thus, each decision in turn determines the scenario further development project.

Simulation modeling (Monte Carlo method)

Risk analysis of investment projects using the Monte Carlo method combines two previously studied methods: sensitivity analysis method and scenario analysis. In simulation modeling, instead of generating best- and worst-case scenarios, a computer generates hundreds of possible combinations of design parameters based on their probability distribution. Each resulting combination produces its own NPV value. Such a calculation is only possible using special computer programs. The phased scheme of simulation modeling is constructed as follows:

• · factors influencing the cash flows of the project are formulated;
• · a probability distribution is constructed for each factor (parameter), and as a rule, it is assumed that the distribution function is normal, therefore, in order to set it, it is necessary to determine only two points (mathematical expectation and variance);
• · the computer randomly selects the value of each risk factor based on its probability distribution;

Fig.1.3

Fig.1.4

The disadvantages of this risk modeling method include:

• · the existence of correlated parameters greatly complicates the model
• · the type of probability distribution for the parameter under study may be difficult to determine
• · when developing real models, it may be necessary to attract outside specialists or scientific consultants;
• · research of the model is possible only with the availability of computer technology and special application software packages;
• · relative inaccuracy of the results obtained in comparison with other methods of numerical analysis.

Discount rate adjustment method

Due to the simplicity of the calculations, the Risk Adjustment Discount Rate Method is the most applicable in practice. This method is an adjustment to a given basic discount rate, considered risk-free and minimally acceptable (for example, marginal cost capital for the company). The adjustment is carried out as follows: the amount of the required risk premium is added, then the criteria for the effectiveness of the investment project are calculated (NPV, IRR, PI). The decision on the effectiveness of the project is made according to the rule of the selected criterion. The higher the risk, the higher the premium.

Risk adjustments are set separately for each individual project, since they completely depend on the specifics of the project under study.

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Introduction

1.1 Introductory remarks

1.4.2 Risk management system

Chapter 2. Modeling the process of managing operational risk of credit institutions

2.1 Mathematical formulation of the problem

2.2 Modeling loss amounts

2.3 Modeling of dependent structures of random variables. Copula functions

2.4 Modeling loss frequencies

2.5 Stochastic Monte Carlo model of random approximation

2.6 Calculation of risk capital 66

Chapter 3. Implementation of an operational risk management system

3.1 Development and implementation of an operational risk management system

3.2 Calculation of risk capital

3.3 Assessment of economic efficiency and sustainability of the model

Conclusion

List of used literature

Applications

Introduction

mathematical operational risk economic

Economic and mathematical modeling is now at a stage where a qualitative leap is ripe. All over the world it has accumulated great amount various models. Whatever area of ​​economics we take, there will always be a whole range of mathematical, computer, verbal and meaningful models that relate to it in one way or another. Hundreds scientific journals monthly publish descriptions of new models, or modifications and developments of old ones.

All of them, although called economic models, are actually models of one particular area of ​​the economy and explain one thing. Each of them contributes to the system of knowledge about the economy. The peculiarity of the process of understanding and cognition by a person of complex phenomena is their simplification, reduction to a simple image. Therefore, since knowledge is infinite, the creation of models also, apparently, has no limit.

Within the framework of mathematical economics, using formal means, the study of complex economic mechanisms already encounters significant difficulties. The models are no longer as beautiful and complete as in classical cases, although they consider the most common or most economically feasible combinations of simple mechanisms.

From a practical point of view, any, even very a large number of information in itself has no value. Data in its pure form is not the kind of knowledge that is called “power”. Information becomes power when it allows you to foresee the future, i.e. answer the main question when choosing a solution: “What will happen if?” To answer this question, in addition to data, you need to have a model of the real world.

Where do models come from and why are they practically absent from banking management systems? In the banking business, the process of creating adequate models is complicated by two objectively existing factors. The first is that from a management point of view, a bank is an extremely complex object, consisting of many different subsystems, between which there are a large number of heterogeneous connections. The bank's activities consist of a number of business processes that significantly depend on many external factors: legislative, economic, social, political.

In cybernetics, objects such as a bank are called complex systems, and the methods for studying them are called systems analysis methods. The most significant results in this area are associated with operations research, an approach based on the use of quantitative mathematical methods to evaluate decisions. However, the use of quantitative methods is possible only in the case when the researcher has adequate mathematical models, which are precisely absent in banking.

The second factor is manifested in the fact that in banking (especially in the context of transition to a market), it is impossible to conduct targeted experiments that precede the formation of a hypothesis and allow it to be tested in practice. Analysts' accumulation personal experience impedes the dynamic change in the situation typical of modern Russia.

More than anything financial science is associated with the analysis of the profitability of investment activities. In addition to measuring profitability, bank analysts also deal with the uncertainty of income generation; Risk analysis is associated with this uncertainty. The lack of development of these issues in our practice explains the need to study foreign experience in terms of its application in Russia.

The set of indicators, methods and calculation models used in assessing the profitability of a particular banking strategy is the subject of new, dynamically developing scientific directions-- financial mathematics and financial analysis, formed at the intersection modern theory finance and a number of mathematical disciplines, such as: econometrics, probability theory, mathematical statistics, operations research, theory of random processes.

The main goal of banking is to maximize profits; An almost equivalent task is also to minimize banking risks. Declining profit margins from banking operations, a shrinking customer base and a decrease in turnover on customer accounts lead to the fact that the ratio between a bank's profit and its operating costs becomes extremely unfavorable. Thus, a situation is created where banks are forced to look for ways to reduce costs and minimize risks. And this, in turn, forces banks to convert Special attention on the financial analysis and methods of managing your resources.

The ability to take reasonable risks is one of the elements of the culture of entrepreneurship in general, and banking in particular. In market conditions, each of its participants accepts certain rules of the business game and, to a certain extent, depends on the behavior of its partners. One of these rules can be considered the willingness to take risks and take into account the possibility of its implementation in one’s activities.

One of the main types of risks of credit institutions is operational risk, caused by the uncertainty of the state and functioning of their internal and external environment. Losses from the occurrence of operational risk events can lead to significant direct and indirect losses, ruin of companies and even loss of life. High-profile bankruptcies recent years, which were caused, among other things, by errors in the organization of the operational risk management system, indicate the scale and insufficient elaboration of the issues of assessing, preventing and minimizing losses from the occurrence of events related to operational risk. The lack of representative statistical information, the heterogeneous and individual profile of operational risk for each credit organization makes it impossible to use generally accepted methods and models for measuring and managing financial risks used in the theory of risk management for the analysis and management of operational risk.

The need to reserve capital for operational risk (inclusion of operational risk in the calculation of the capital adequacy ratio H1) became a reality for Russian commercial banks already in August 2010, as this reflects the development strategy of the banking sector and the course of the Central Bank of the Russian Federation towards the introduction of risk-based approaches in assessing credit organizations.

Thus, the construction tasks effective system measuring, forecasting and minimizing operational risk arising in the course of the activities of credit institutions determine the relevance of the study.

The purpose of the study is to develop methods and models for integrated management of operational risk of credit institutions. In accordance with this goal, the following tasks were set and solved:

1. Conduct research existing models and methods of analysis and management of financial risks in relation to the specifics of operational risk.

2. Develop a comprehensive classification of events and operational risk factors, taking into account the specifics of the activities of credit institutions.

3. Develop mathematical tools necessary for the analysis, measurement and management of operational risk, including:

· pose and implement the problem of mathematical modeling of random processes of loss occurrence, taking into account the presence of the effect of correlations between them;

· develop and programmatically implement a stochastic algorithm for modeling the total amount of losses with a given structure of dependencies and calculating the amount of risk capital to cover them (taking into account the availability of various insurance coverages and risk measures).

4. Develop a software implementation for modeling the process of managing operational risk of a credit organization, assess the sensitivity of the implemented methods to various disturbances of input parameters.

5. Determine the economic efficiency of the implemented operational risk management model. Develop guidelines on organizing the process of operational risk management in credit institutions.

The object of the thesis research is operational risks arising during current activities credit organizations. The subject of the diploma research is economic and mathematical methods and models of the operational risk management process as an element of the risk management system of a credit organization.

Theoretical and methodological basis The research included the works of domestic scientists in the field of insurance, financial and actuarial mathematics, game theory, probability theory and mathematical statistics, the theory of extreme values, random processes, numerical methods, and risk management.

The scientific novelty of the research lies in the development of an integrated approach to operational risk management based on the synthesis of the following tasks of economic and mathematical modeling: analysis of the processes of loss occurrence, assessment of the total amount of losses, calculation of the amount of risk capital to cover them. The subject of protection is the following provisions and results containing elements of scientific novelty:

1. The problem of mathematical modeling of random processes of occurrence of losses of credit institutions associated with operational risk has been posed and solved, allowing for a more accurate assessment of the magnitude of operational risk compared to existing calculation methods.

2. Probabilistic modeling of the aggregated amount of losses has been implemented, taking into account the presence of correlations between them, which makes it possible to more accurately estimate the total amount of losses and to reasonably reduce the estimated amount of the required risk capital to cover them.

3. A software implementation has been developed for stochastic modeling of the amounts of random processes (losses) with a predetermined structure of dependencies and calculation of the amount of capital to cover them, taking into account the availability of various insurance programs and risk measures. The sensitivity of the developed methods to various disturbances of input parameters was assessed.

4. The economic efficiency of using the developed comprehensive operational risk management model in credit institutions has been proven in comparison with existing methods and models of analysis and management of operational risk (in terms of saving the amount of risk capital).

The first chapter discusses the features of simulation modeling of banking processes, the bank's functioning model, the concept of risk in banking, the classification of banking risks and the risk management system.

In the second chapter, the problem of mathematical modeling of the processes of occurrence of losses of credit institutions associated with operational risk is posed and solved. Mathematical models and methods for assessing, measuring and forecasting the total amount of aggregated losses, calculation and coherent distribution of the amount of risk capital have been implemented; a mechanism for supplementing one’s own data by mapping information about losses has been proposed external organizations, the effect of the term structure of money and the presence of a significance threshold was taken into account when modeling the amount of losses. The third section of the chapter presents the basic facts of copula theory, necessary for modeling dependent random processes, and discusses correlation measures invariant to monotonic transformations. An algorithm for stochastic modeling of random processes with known distribution functions and a predetermined dependence structure using a Gaussian copula has been implemented. Using copula theory, an algorithm for generating dependent processes that model the frequency of losses is implemented. Section 2.5 describes a stochastic Monte Carlo model, developed and implemented in MATLAB, to estimate the probability distributions of a credit institution's cumulative losses for the general case, using Gaussian and Student's t-copulas and fast Fourier transform. This model formed the basis of the AMA model, the results of its implementation are discussed in the third chapter. As an alternative to the Basel II quantile VaR function for calculating the amount of capital to cover operational risk, section 2.6 proposes the use of coherent risk measures. A measure (Expected ShortFall - ES) is considered that satisfies the subadditivity condition, allowing us to obtain results that are more resistant to various extreme distributions of loss values. The problem of coherent distribution of risk capital between areas of activity and/or divisions of a credit institution has been formulated and solved. The result obtained is that in terms of non-atomic game theory, the principle of coherent distribution of risk capital can be uniquely defined through the Aumann-Shapley vector, which always exists and belongs to the core of the game.

The third chapter develops the main implementation stages and information support for the integrated operational risk management system of a credit institution. The key points in the creation of internal regulations and methodologies regulating the process of operational risk management, which are subject to mandatory coverage in accordance with the requirements of the Central Bank of the Russian Federation and Basel II recommendations, are given. In addition to the calculations quantitative indicators operational risk, it is recommended to monitor qualitative indicators of operational risk that best characterize the main areas of activity of the credit institution that are exposed to operational risk. Section 3.1 develops a comprehensive system of indicators (KIR - key risk indicators) for medium-sized credit institutions.

As a demonstration of the developed quantitative methods for managing operational risk, in the second part of the third chapter, a simplified implementation of the AMA model is considered using the example of calculating the CaR value for a medium-sized credit bank. A comparison of risk capital values ​​calculated on the basis of different approaches and for different risk measures and significance levels. In Section 3.3, the sensitivity of the implemented model is analyzed for various perturbations of the input parameters. An assessment of the expected economic effect from the implementation of developed models and methods for managing operational risk of credit institutions in comparison with existing approaches.

In conclusion, the main results obtained and conclusions of the study are formulated.

Chapter 1. Analysis of existing mathematical models of the bank

1.1 Introductory remarks

As mentioned above, the main goal of banking is to maximize profits; An almost equivalent task is also to minimize banking risks. This means that the policy of a commercial bank should be based on a thorough assessment and simulation of various situations, analysis of many factors affecting the amount of profit. These factors determine the level of banking risk; The bank's task is to minimize it.

Bank profitability = Profitability of credit resources + Return on investment:

Where -- specific gravity th and th type of resources,

DB - bank profitability,

KR - credit resources,

Central Bank - investments in securities.

Investors purchase assets, such as stocks, bonds, or real estate, with the goal of generating income either by selling them at a higher price or in the form of dividends, coupon interest, or rent payments. Lenders lend money in hopes of earning a return on interest payments when the borrower repays the loan in full. Thus, lenders and investors have common goal-- receive income or interest as a result of investment or lending activities.

Declining profit margins from banking operations, a shrinking customer base and a decrease in turnover on customer accounts lead to the fact that the ratio between a bank's profit and its operating costs becomes extremely unfavorable. Thus, a situation is created where banks are forced to look for ways to reduce costs and minimize risks. And this, in turn, forces Russian banks to pay special attention to financial analysis and methods of managing their resources.

The most important rule on which decision-making strategies are based under risk conditions in business:

Risk and return move in the same direction: the higher the return, the higher the risk of the operation, as a rule.

If banks want to raise additional funds, they must demonstrate to their clients that they have fully taken into account the risk-return ratio.

It is this thesis that is currently used in a number of the largest foreign banks.

Under the conditions of a planned economy, the understanding of risk and uncertainty as integral components of socio-economic development, as the most important scientific categories requiring comprehensive study, was excluded. The formation of market relations and corresponding economic mechanisms in Russia has led to the return of the concept of risk to the theory and practice of managing economic objects of all levels and forms of ownership.

Much attention is paid to modeling banking processes abroad. The idea of ​​banking portfolio management or end-to-end balance sheet management has its origins in modern portfolio theory, developed in the mid-50s. The first attempts to apply modern portfolio theory to banking took the form of linear and quadratic mathematical programming models. Although these models were quite slender in the classical sense, they were too limited and complex for practical use. Their main value is the ability to gain insight into complete balance management. It is useful as an aid to understanding how to manage a banking portfolio and risk.

Portfolio management concepts are illustrated using a linear programming model. Of course, in order to reduce reality to a two-dimensional problem, we had to seriously simplify the formulation of the problem.

Let's present the bank's balance sheet in the following simplified form:

where Central Bank are securities,

KR - loans,

DV - demand deposits,

SD - time deposits,

K - capital. Egorova N.E., Smulov A.S. Enterprises and banks: interaction, economic analysis and modeling.-M.; Delo, 2002. P.61.

Profit on securities and profit on loans will be denoted by P cb and P cr, respectively. The costs of attracting deposits and capital are assumed to be zero. Hence, the income or profit of the bank Pr is given by the equation:

We also give a classification of analytical programs for banking activities:

1. Level in organizational structure bank: senior management, middle level, performers.

2. Type of transaction being analyzed: credit transactions, securities, currency operations, other operations.

3. Type of problem to be solved: monitoring, analysis, optimization, modeling, forecast, planning, control.

4. Time lag of analysis: current moment, short-term estimates, medium-term estimates, long-term estimates.

1.2 Features of simulation modeling of banking processes

The need to use simulation modeling is due, first of all, to the features Russian market. A distinctive feature of Russian financial market-- its “subjectivism”, extreme dependence on non-economic factors and, as a result, a high degree of uncertainty, which makes it difficult to make informed financial decisions.

This uncertainty is created by:

1. instability of the external environment of Russian banks, lack of clearly established rules and procedures for organizing various sectors of the financial market (institutional aspect);

2. lack of a sufficiently developed apparatus for forecasting the macroeconomic situation in uncertain conditions and analyzing the multiplicity of factors (instrumental aspect);

3. the impossibility of taking into account and formalizing all connections to build an economic and mathematical model that adequately reflects the structure of the financial market (cognitive aspect);

4. inaccessibility of reliable information - lack of a single information space “bank - client - financial market - state” (information aspect);

5. inadequate reflection of the real financial condition bank in financial statements(balance sheet, etc.) and, thus, the lack of financial transparency in the bank (accounting aspect). The use of traditional means of supporting management decisions and forecasting in these conditions is difficult, and the more valuable is the opportunity to use the simulation modeling method. Emelyanov A.A. Simulation modeling in risk management. - St. Petersburg: St. Petersburg Academy of Engineering and Economics, 2000. P.132.

Many modern software products are designed specifically to predict the situation on the financial market. These include tools for technical analysis of the stock market, expert systems and statistical packages. These products are aimed primarily at decision makers in the government debt market.

Practice of application by banks and investment companies forecasting tools in market trading valuable papers shows that the forecast is not always reliable even from the point of view of the trend. One of the reasons for this is the limited period of statistical observations.

In turn, simulation modeling is a tool with which you can cover all areas of the bank’s activities: credit and deposit, stock, work with foreign exchange assets. The Bank Simulation Model (BSM) does not predict market behavior. Its task is to take into account the maximum possible number of financial factors of the external environment (currency market, securities market, interbank loans, etc.) to support financial decision-making at the level of the bank manager, treasury, and asset and liability management committee.

In this sense, the MPI in its functions is closely related to the developed automated banking systems(ABS) of Western design, which are used by large international merchant banks.

Modeling processes in a bank allows you to simulate the registration of banking transactions and take into account the information that the transaction contains. The use of this construction ideology is completely justified not only from the point of view of simulating real financial flows in a bank, but also from the point of view of the practical applicability of modeling results in the activities of a bank financial manager.

Indeed, the balance sheet turns out to be a secondary result of decisions made. Both in practice and in the MPI, a manager, when making a decision on a transaction, assesses its risks and consequences for the bank not at once, but throughout the entire life cycle of the transaction.

Simulation models are an integral part of modern banking management. Managing assets and liabilities and planning large-scale operations require reliable analytical techniques.

Simulation modeling systems are widely used for analysis, forecasting and studying of various processes in various fields of economics, industry, scientific research both purely theoretical and practical directions.

The use of such systems is most effective and justified for long-term forecasting and in situations where conducting a practical experiment is impossible or difficult. Simulation modeling is information technology, which works with a simulation model and allows one to evaluate its parameters (hence, efficiency) in an accelerated time scale.

Simulation model -- software, allowing you to simulate the activity of any complex object. Sometimes the objects being simulated can be so complex, and have so many parameters, that creating a simulation model in a standard high-level programming language may take too much time to justify the results. Emelyanov A.A. Simulation modeling in risk management. - St. Petersburg: St. Petersburg Engineering and Economic Academy, 2000. P.24

There are many tasks and situations that require the use of simulation technologies. These include modeling bank operating scenarios, “testing” certain decisions, analyzing alternative strategies, and much more. A qualified specialist is able to cite dozens of standard and specific problems that require analytical techniques. These include both classic tasks of banking planning and tasks of “home” origin, for example, coordinating schedules of obligations and receipts. Simulation models make it possible to make both approximate estimates and express audits of decisions made, as well as detailed numerical forecasts and calculations. Quick analysis of the situation based on a compact model of medium complexity is a valuable opportunity for any bank manager.

Simulation models make it possible to link the activities of all bank divisions into a single whole. On this basis, it becomes possible to effectively organize the entire system of operational and strategic planning commercial bank. Thanks to the use of streaming approaches, information about the activities of the bank and its services takes on a concise and easy-to-read form. It lends itself to quantitative and qualitative (content) analysis. A simulation model based on one of the expert packages is a reliable guide for bank management. The streaming “picture” of the bank’s activities greatly facilitates both operational management and long-term planning of the bank’s work.

Simulation models can be embedded in the basis of the expert complex of a commercial bank. In this case, a simulation model created on the basis of one of the expert packages is connected through data exchange channels with other specialized software packages and spreadsheets databases. Such a complex can operate in real time. In terms of its capabilities, it approaches large, expensive bank management automation systems.

Optimization models, including multicriteria ones, have a common property - a known goal, to achieve which one often has to deal with complex systems, where it is not so much about solving optimization problems, but about studying and predicting states depending on the chosen control strategies. And here we are faced with the difficulties of implementing the previous plan. They are as follows:

1. a complex system contains many connections between elements;

2. the real system is influenced by random factors, which cannot be taken into account analytically;

3. the possibility of comparing the original with the model exists only at the beginning, and after using the mathematical apparatus, since intermediate results may have no analogues in the real system. Emelyanov A.A. Simulation modeling in risk management. -SPB: St. Petersburg Engineering and Economic Academy, 2000. P.58.

Due to various difficulties that arise when studying complex systems, practice required a more flexible method, and it appeared - Simulation modeling.

Typically, a simulation model is understood as a set of computer programs that describes the functioning of individual system blocks and the rules of interaction between them. The use of random variables makes it necessary to carry out repeated experiments with a simulation system (on a computer) and subsequent statistical analysis of the results obtained. A very common example of using simulation models is solving the queuing problem using the Monte Carlo method.

Thus, working with a simulation system is an experiment carried out on a computer. What are the advantages?

1. greater proximity to the real system than mathematical models;

2. the block principle makes it possible to verify each block before its inclusion in the overall system;

3. the use of dependencies of a more complex nature, not described by simple mathematical relationships.

The listed advantages determine the disadvantages:

1. building a simulation model is longer, more difficult and more expensive;

2. to work with the simulation system, you must have a computer suitable for the class;

3. interaction between the user and the simulation model (interface) should not be too complex, convenient and well known;

4. building a simulation model requires a more in-depth study of the real process than mathematical modeling. Emelyanov A.A. Simulation modeling in risk management. -SPB: St. Petersburg Engineering and Economic Academy, 2000. P.79.

The question arises: can simulation modeling replace optimization methods? No, but it conveniently complements them. A simulation model is a program that implements a certain algorithm, to optimize the control of which an optimization problem is first solved.

So, neither a computer, nor a mathematical model, nor an algorithm for its study alone can solve a sufficiently complex problem. But together they represent the force that allows us to understand the world around us and manage it in the interests of man.

Taking into account the complex of tasks facing banking analysts, this system should provide:

1. calculation of indicators of the current and future financial conditions of the bank;

2. forecast of the state of individual financial transactions and the balance of the bank as a whole;

3. assessing the attractiveness of individual financial transactions;

4. synthesis (formation) of management decisions;

5. assessment of the effectiveness of the management decision made;

6. assessment of the completeness and non-redundancy of sets of indicators of the bank’s financial condition.

Performing any of the above functions requires simulation financial activities jar.

1.3 Bank operating model

The range of methods used to analyze and model banking activities is extensive and varied. During the evolution of the mathematical theory of banks, methods of mathematical statistics, optimal control theory, random process theory, game theory, operations research theory, etc. were used. It should be remembered that a bank is a complex entity that requires an integrated approach. It will be extremely difficult to create an integrated bank model that simultaneously covers liquidity management, the formation of an asset portfolio, the formation of a credit and deposit policy, etc., so we will describe the functioning of the bank in a fairly aggregated manner.

Let's consider the bank's operation over a fairly large time interval.

Let the bank receive income in the form of payment for its services for carrying out settlements of guarantee operations, brokerage services (or other income independent of the portfolio of assets) - and income from securities purchased with available funds that together make up the portfolio of banking assets.

Income from purchased securities consists of interest on securities - and payments of invested funds upon redemption or sale of securities -

(in case of promotion

where is the interest rate on purchased securities

average time until maturity of securities purchased by the bank. Kolemaev V.A. Mathematical Economics. - M.: UNITY, 1998. P.68.

The bank also receives borrowed funds from the placement of its securities at a rate of - W. We will assume that the securities issued by the bank are initially placed and redeemed at par, and the interest income on them is determined based on the situation on the financial market at the time of issue .

The bank primarily uses the income received to pay for the costs of raising funds, which consist of interest payments on placed securities - and payments of principal amounts of borrowed funds -

where is the interest rate on placed securities

Average time until maturity of securities issued by a bank.

In addition, the bank incurs expenses independent of the volume of its liabilities - where:

Consumer price index,

To pay for the rental of premises, to pay for telecommunications expenses, as well as other expenses that do not depend on the volume of funds raised (liabilities).

The bank then pays the necessary taxes. The bank uses the remaining funds to invest in its own infrastructure (internal investments) - and for dividend payments -.

The fact that the bank is obliged to pay some expenses from its net profit can be taken into account by increasing the amount of expenses by dividing by (1-tax rate). There are also taxes levied on amounts of income regardless of the costs incurred to generate that income, such as the highway user tax. Such taxes can be taken into account by multiplying the amount of income in advance by (1-tax rate). Similar methods can also take into account other features determined by tax deductions, so we will not consider below the problems associated with taxation and tax benefits for some securities, such as government securities. Please note that expenses are paid by the bank in a certain order. First of all, the bank is obliged to redeem previously issued securities and pay interest on them, then it pays expenses that do not depend on the volume of liabilities, taxes, and only after that can pay dividends.

If the bank has free funds, then it uses them to purchase securities (external investments) at a speed of -. In case of insufficient funds, the securities in the bank's portfolio can be sold, then it has a negative sign. Artyukhov S., Bazyukina O.A., Korolev V.Yu., Kudryavtsev A.A. An optimal pricing model based on risk processes with random premiums. // Systems and means of computer science. Special issue. - M.: IPIRAN, 2005. P.102

The amount of money, securities purchased by the bank and securities placed by the bank changes over time as follows:

where is the expenditure of money on the purchase of securities (money received from their sale), and is a fairly small time constant characterizing the quality of the bank’s assets, in the sense of liquidity. If a bank places all its assets in any one segment of the financial market, then there is a value for it that characterizes the degree of development of this segment. In the general case, it is obtained as a weighted average by the volume of assets from the values ​​characterizing the degree of development of each of the financial market segments in which the assets are located. Since we do not consider the problem of asset formation in this work, A is assumed to be a given value.

The maximum amount of funds that a bank can attract by placing its own securities is limited and depends mainly on the volume of the bank’s own capital, the structure of its balance sheet, the quality of the bank’s investment portfolio and other less important factors. important indicators his works. We will assume that

where is the bank's reliability coefficient,

Volume own funds jar.

The bank's placement of its own securities to attract borrowed funds also takes place with some limited speed, That's why

where is a time constant characterizing the degree of development of the market for other securities issued by the bank. It depends on how developed the bank’s infrastructure is and how large the number of market participants with whom the bank cooperates.

Let's introduce a variable - the value of the portfolio of purchased securities. Then equations (1.4) - (1.6) will take the form

Let us introduce dimensionless controls: through which the rate of spending money on the purchase of securities and the rate of receipt of money from the placement of bank securities are expressed as follows:

The value corresponds to the purchase/sale of securities of third-party issuers as quickly as the efficiency of the securities market allows. The value corresponds to the bank’s fastest raising of borrowed funds, and to a complete refusal to raise funds.

The main feature of money, which makes it significantly different from securities purchased by a bank, even government securities, is the ability to use it to pay for the bank’s current expenses. The flow of payments cannot be carried out if there is not a sufficient supply of money, therefore, the speed of payments is limited and depends on the volume of money:

where is the characteristic time of arrival at the bank Money(making payments). Restrictions of this type are called liquidity restrictions.

Payments made by the bank must be divided into two groups:

Obligatory payments. These include payments for the redemption of securities issued by the bank - payment of interest on securities - expenses that do not depend on the volume of liabilities - In practice, the bank may delay mandatory payments, but this will lead to serious financial losses, and with a long delay, to the recognition of it insolvent and eventually to liquidation. We will assume that delays in mandatory payments are completely excluded, i.e., the bank is required to constantly maintain liquidity.

Optional payments. Making these payments depends on the management and owners of the bank. These include domestic investment - and dividends - рС 2 .

To maintain liquidity, the bank must:

for everyone (1.11)

Thus, we obtain the first phase constraint for our problem - condition (1.11).

Note that from this inequality, under the condition of non-negativity in particular, it follows that for all

Making optional payments is also limited in speed:

According to this inequality, one can introduce dimensionless control so that:

Since the bank’s retention of its share in the financial services market depends on the volume of domestic investments, expenses can be classified, in a sense, as mandatory, at least in most of the planning area. (After reaching the planning horizon T, the bank can be liquidated by its owners). Since dividend payments cannot be negative, we get another phase constraint:

for everyone (1.13)

Thus, we have come to the conclusion that domestic investment is indeed obligatory in the sense of constraint (1.13).

We will assume that in the planning area the bank does not receive “excess income,” i.e., large profits compared to its own capital, independent of the volume of assets. Consequently, the maximum amount of money that he can attract and receive in the form of profit is limited by some constant, i.e. for all and this is the third phase constraint (1.14).

The assessment can be obtained based on the maximum volume of borrowings, the ratio of interest rates on attracting and placing funds, the volume of income that does not depend on the amount of assets -.

Note that in most of the planning area it should be close to zero, since it is not profitable for the bank to hold cash that does not generate income, because the financial market always has absolutely reliable government securities that generate a fixed positive income.

The absence of “excess income” also means that in the planning area the relative rate of growth of securities prices is limited:

We will describe the interests of the bank (its owners) by the desire to maximize the discounted utility of future dividend payments over a sufficiently large time interval. We will assume that the utility obtained from immediate payment appears to be times greater than the utility of payment of the same amount of funds, taking into account inflation, but over time . The coefficient is called the discount factor for the utility of dividend payments. Then the maximized functional is written in the following form:

where is the utility function of dividend payments.

When utility of consumption plays a role, it is usually required that it be continuous, monotonic, concave and bounded from above, and is also imposed on the condition The last condition guarantees that current consumption is positive at each point in time. Since dividends may not be paid, we will not require the condition to be satisfied, assuming that the utility function has a low aversion to zero consumption.

If the utility function has Arrow-Pratt constant relative risk aversion: then it can be shown that it can be written as:

To get rid of the high aversion to zero consumption, consider a slightly modified utility function

In this case, relative risk aversion will depend on the volume of consumption: . Based on (1.9) and (1.11) we obtain

Let us consider instead of function (1.13) a straight line passing through the points

Since function (1.17) will be negative for any volume of dividends, i.e., bounded from above by zero, and also continuous and monotonic for any. Such a utility function has zero Arrow-Pratt relative risk aversion, and by varying the parameter one can only change the nominal value of dividend payments. This fact highlights the differences in risk attitudes between private consumers and commercial organization. On the one hand, the latter does not have an aversion to risk, since it can exist indefinitely, compared to the lifespan of a person, and is not subject to dangers, like living beings. On the other hand, a private consumer who has spent the amount of 2*M rubles receives greater satisfaction from the first M rubles spent than from subsequent ones, which determines the concavity of the consumption utility function for individuals. We will assume that doubling dividend payments leads to doubling their utility for recipients, who are quite numerous and include both individuals and legal entities. This determines the linearity of the utility function of dividend payments. In what follows we will use the utility function (1.17).

Thus, we obtain the optimal control problem in continuous time

In addition, there is a boundary condition which means that the bank is obliged to repay its debt by the end of the planning period.

Here are phase variables and controls. Here - the predicted values ​​of the corresponding variables - are considered given non-negative functions of time, - constants having the dimension of time.

Note that if at some point it vanishes, then according to equation (1.21), i.e. the solution at this point does not decrease. Accordingly, if at some point it reaches a value, then the solution does not increase. Thus, with controls, from equation (1.21), conditions and continuity, we obtain that throughout the entire segment, the volume at par of the bank’s placed securities is non-negative, i.e., and does not exceed the permissible maximum - , for all (generally speaking on ).

Then, from the condition and conditions of non-negativity of the given functions, as well as non-negativity, we obtain that for all. Assuming continuity, it can be shown using equation (1.20) that for all. Further we will |assume that and are continuous and piecewise continuous on.

Since it also follows from equation (1.20) that. Using this inequality, it is easy to show the existence of such that, for everyone.

We will not, as previously assumed, consider how exactly the portfolio of securities purchased by the bank is formed, depending on the reliability, profitability and liquidity of the latter, as well as on the preferences of the bank’s management. All bank assets will be presented in aggregate form - one variable.

From the above it is clear that the bank’s credit and deposit policy, determined in the model by management, is inextricably linked with the policy of dividend payments set by management, so further we will study them together.

For the convenience of further study of the work, we write out the notation separately:

The volume of free funds of the bank - cash banknotes in the bank's cash desk, or money held in the correspondent. bank accounts in the settlement centers of the Central Bank of the Russian Federation, as well as on the correspondent. accounts in other banks

Volume of purchased securities at par

Volume of placed securities at par

Income independent of the volume of assets (commissions for cash management services, guarantee transactions, brokerage services, etc.)

Planning horizon

Volume of the bank's own funds (capital)

Bank reliability coefficient

The speed at which the bank spends funds on maintaining the management staff, paying for the rent of premises, etc. or expenses independent of the volume of bank liabilities in prices at the initial point in time

The rate of reinvestment in the bank’s infrastructure (domestic investment) in prices at the initial point in time

The speed of dividend payments in prices at the initial point in time

Current market rate of securities purchased by the bank

Market value of the bank's securities portfolio

Time constant characterizing the degree of development of the financial market, taking into account the distribution of bank assets across its sectors

Time constant characterizing the degree of development of the market for securities issued by the bank

Nominal growth index of the securities portfolio acquired by the bank. For each purchased security, the nominal rate is reduced to the annual rate, taking into account reinvestment, then the weighted average annual rate is calculated for all securities in the bank’s portfolio. The index is defined as ln (1 + “weighted average annual rate”)

Effective growth index of the securities portfolio acquired by the bank

Index of growth of total debt on placed securities. For each placed security, the nominal rate is reduced to the annual rate, taking into account debt refinancing through new placements of securities, then the weighted average annual rate for all placed securities is calculated. The index is defined as ln (1 + + “weighted average annual rate”)

Average time to repay securities purchased by a bank - average time to repay securities issued by a bank - consumer price index

Inflation index

Typical time of payments (receipt of funds)

Speed ​​of circulation of money in the banking system

The speed of spending money on the purchase of securities of third-party issuers, or the receipt of money from their sale

The rate of receipt of money from the placement of bank securities

Discount factor for the utility of dividend payments

Relative risk aversion according to Arrow-Pratt, a parameter used to specify the utility function of dividend payments

M* - the maximum amount of money that can belong to the bank

Utility function of dividend payments, continuous, monotonic

Management of bank dividend payments

Management of the placement of free funds of the bank

Managing the attraction of funds to the bank.

1.4 The concept of risk in banking

Risk is the possible danger of some unfavorable outcome.

In market conditions, each of its participants accepts certain rules of the game and, to a certain extent, depends on the behavior of their partners. One of these rules can be considered the willingness to take risks and take into account the possibility of its implementation in one’s activities.

Risk is usually understood as the probability, or more precisely the threat, of a bank losing part of its resources, losing income, or the appearance of additional expenses as a result of certain financial transactions. Shchelov O. Operational risk management in a commercial bank. Accounting and banks, 2006 - No. 6. P.112

In a crisis, the problem professional management banking risks, prompt accounting of risk factors are of paramount importance for financial market participants, and especially for commercial banks.

The leading principle in the work of commercial banks in the transition to market relations is the desire to obtain as much profit as possible. The higher the expected profitability of the operation, the greater the risks. Risks arise as a result of deviations of actual data from the assessment of the current state and future development.

The modern banking market is unthinkable without risk. Risk is present in any operation, only it can be of different scales and “mitigated” and compensated for in different ways. It would be extremely naive to look for options for carrying out banking operations that would completely eliminate risk and would guarantee a certain financial result in advance.

1.4.1 Classification of banking risks

In the course of their activities, banks are faced with a combination of various types risks that differ from each other in place and time of occurrence, external and internal factors, influencing their level, and, consequently, the methods of their analysis and methods of their description. Lobanov A.A., Chugunov A.V. Encyclopedia of financial risk management. - M., Alpina Business Books, 2005. P.89. All types of risks are interconnected and affect the bank’s activities.

Depending on the sphere of influence or occurrence of banking risk, they are divided into external and internal.

External risks include risks not related to the activities of the bank or a specific client, political, economic and others. These are losses arising as a result of the outbreak of war, revolution, nationalization, ban on payments abroad, debt consolidation, embargo, cancellation of import licenses, aggravation of economic crisis in a country affected by natural disasters. Internal risks, in turn, are divided into losses from the main and auxiliary activities of the bank. The first represent the most common group of risks: credit, interest, currency and market risks. The second includes losses on the formation of deposits, risks from new types of activities, and risks of banking abuse.

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The textbook outlines the essence of uncertainty and risk, classification and factors affecting them; Methods for qualitative and quantitative assessment of economic and financial situations under conditions of uncertainty and risk are provided.

A classification of service technologies is given, examples of the activities of service organizations in risk situations are considered.

The methodology for managing investment projects under risk conditions is outlined, recommendations are given for managing an investment portfolio, the financial condition and development prospects of the investment object are assessed, and a model for taking risks into account in investment projects is proposed.

Considerable attention is paid to methods and models of management under risk conditions and the psychology of behavior and assessment of the decision maker.

For undergraduate and graduate students of economic universities and faculties, students of business schools, risk managers, innovation and investment managers, as well as banking and financial structures, employees of pension, insurance and investment funds.

Chapter 1 PLACE AND ROLE OF ECONOMIC RISKS IN THE ACTIVITIES OF ORGANIZATIONS

1.2. PLACE AND ROLE OF RISKS IN ECONOMIC ACTIVITY

1.3. RISK MANAGEMENT SYSTEM

Chapter 2 RISKS OF SERVICE COMPANIES

Chapter 3 INFLUENCE OF MAIN FACTORS OF MARKET EQUILIBRIUM ON RISK MANAGEMENT

3.2. INFLUENCE OF MARKET EQUILIBRIUM FACTORS ON CHANGES IN RISK

Chapter 4 FINANCIAL RISK MANAGEMENT

4.1. FINANCIAL RISKS

4.2. INTEREST RISKS

4.4. RISK INVESTMENT PROCESSES

4.5 CREDIT RISKS

4.7. INFLATION RISK

4.8. CURRENCY RISKS

4.9. RISKS OF ASSETS

Chapter 5 QUANTITATIVE ESTIMATES OF ECONOMIC RISK UNDER UNCERTAINTY

5.2. MATRIX GAMES

5.5. MULTICRITERIAL PROBLEMS OF SELECTION OF EFFECTIVE SOLUTIONS

5.7. DETERMINING THE OPTIMAL VOLUME OF PRODUCTION OF A GARMENTING ENTERPRISE UNDER CONDITIONS OF UNCERTAINTY

Chapter 6 OPTIMAL DECISION MAKING IN CONDITIONS OF ECONOMIC RISK

6.5. SELECTION OF THE OPTIMAL PLAN USING THE METHOD OF CONSTRUCTION OF EVENT TREES

6.6. COMPARATIVE ASSESSMENT OF SOLUTION OPTIONS

6.8. ACTIVITY OF SERVICE COMPANIES UNDER CONDITIONS OF RISK

Chapter 7 MANAGEMENT OF INVESTMENT PROJECTS UNDER CONDITIONS OF RISK

7.1. INVESTMENT PROJECTS IN CONDITIONS OF UNCERTAINTY RISK

7.3. INVESTMENT IN SECURITIES PORTFOLIO

7.4. ANALYSIS OF THE ECONOMIC EFFICIENCY OF AN INVESTMENT PROJECT

7.5. ACCOUNTING RISK IN INVESTMENT PROJECTS

Chapter 8 RISK MANAGEMENT OF TOURISM

8.2. PSYCHOLOGY OF THE IMPACT OF TOURISM ON PARTICIPANTS AND AROUND

8.3. RISKS ASSOCIATED WITH TOURISM ACTIVITIES

Chapter 9 RISK MANAGEMENT OF HOTELS AND RESTAURANTS

9.4. RISKS INHERENT IN THE HOSPITALITY INDUSTRY AND THEIR MANAGEMENT

Name: Risk theory and modeling of risk situations.

The textbook outlines the essence of uncertainty and risk, classification and factors affecting them; Methods for qualitative and quantitative assessment of economic and financial situations under conditions of uncertainty and risk are provided.

A classification of service technologies is given, examples of the activities of service organizations in risk situations are considered.

The methodology for managing investment projects under risk conditions is outlined, recommendations are given for managing an investment portfolio, the financial condition and development prospects of the investment object are assessed, and a model for taking risks into account in investment projects is proposed.

Considerable attention is paid to methods and models of management under risk conditions and the psychology of behavior and assessment of the decision maker.

For undergraduate and graduate students of economic universities and faculties, students of business schools, risk managers, innovation and investment managers, as well as specialists from banking and financial institutions, employees of pension, insurance and investment funds.

Content
Preface
Chapter 1 THE PLACE AND ROLE OF ECONOMIC RISKS IN MANAGING THE ACTIVITIES OF ORGANIZATIONS
1.1. Organizations, types of enterprises, their characteristics and goals
1.2. Place and role of risks in economic activity
1.2.1. Definition and essence of risks
1.2.2. Management of risks
1.2.3. Risk classification
1.2.4. System of uncertainties
1.3. Risk management system
1.3.1. Management activities
1.3.2. Risk management
1.3.3. Risk Management Process
1.3.4. Mathematical methods economic risk assessments
Chapter 2. RISKS OF SERVICE COMPANIES
2.1. Service technologies
2.2. Classification of risks of service sector enterprises
2.3. Dynamic analysis of the situation in the services market
2.4. Risk management model for service organizations
Chapter 3. INFLUENCE OF MAIN FACTORS OF MARKET EQUILIBRIUM ON RISK MANAGEMENT
3.1. Risk Limiting Factors
3.2. Influence of market equilibrium factors on risk changes
3.2.1. The relationship between market equilibrium and commercial risk
3.2.2. The influence of market equilibrium factors on changes in commercial risk
3.2.3. Modeling the process of achieving equilibrium
3.2.4. The impact of changes in demand on the level of commercial risk
3.2.5. The impact of changes in supply on the degree of commercial risk
3.2.6. Constructing dependencies between demand and supply
3.3. Influence of the time factor on the degree of risk
3.4. The influence of elasticity factors of supply and demand on the level of risk
3.5. The influence of the tax factor in market equilibrium on the level of risk
Chapter 4. FINANCIAL RISK MANAGEMENT
4.1. Financial risks
4.1.1. Classification of financial risks
4.1.2. Communication between financial and operating leverage with total risk
4.1.3. Development risks
4.2. Interest risks
4.2.1. Types of interest risks
4.2.2. Operations with interest
4.2.3. Average percentages
4.2.4. Variable interest rate
4.2.5. Interest rate risks
4.2.6. Interest rate risk of bonds
4.3. Risk of losses from changes in the flow of payments
4.3.1. Equivalent streams
4.3.2. Payment flows
4.4. Risky investment processes
4.4.1. Investment risks
4.4.2. Return rates on risky assets
4.4.3. Net present value
4.4.4. Annuity and sinking fund
4.4.5. Investment Valuation
4.4.6. Risky investment payments
4.4.7. Time discounting
4.5. Credit risks
4.5.1. Factors contributing to credit risks
4.5.2. Credit risk analysis
4.5.3. Techniques for reducing credit risks
4.5.4. Loan payments
4.5.5. Accumulation and payment of interest on a consumer loan
4.5.6. Credit guarantees
4.6. Liquidity risk
4.7. Inflation risk
4.7.1. Relationship between interest rate and inflation rate
4.7.2. Inflation premium
4.7.3. The influence of inflation on various processes
4.7.4. Measures to reduce inflation
4.8. Currency risks
4.8.1. Currency conversion and interest accrual
4.8.2. Exchange rates over time
4.8.3. Reducing currency risks
4.9. Asset risks
4.9.1. Exchange risks
4.9.2. Impact of Default Risk and Asset Value Taxation
4.10. Probabilistic assessment of the degree of financial risk
Chapter 5. QUANTITATIVE ASSESSMENTS OF ECONOMIC RISK UNDER UNCERTAINTY
5.1. Methods for making effective decisions under conditions of uncertainty
5.2. Matrix games
5.2.1. Concept of playing with nature
5.2.2. Subject of game theory. Basic Concepts
5.3. Performance criteria under conditions of complete uncertainty
5.3.1. Guaranteed result criterion
5.3.2. Optimism criterion
5.3.3. Pessimism criterion
5.3.4. Savage's minimax risk criterion
5.3.5. Hurwitz's generalized maximin (pessimism - optimism) criterion
5.4. Comparative assessment of solution options depending on performance criteria
5.5. Multicriteria problems of choosing effective solutions
5.5.1. Multicriteria problems
5.5.2. Pareto optimality
5.5.3. Selecting solutions in the presence of multicriteria alternatives
5.6. Model of decision making under conditions of partial uncertainty
5.7. Determining the optimal volume of garment production under conditions of uncertainty
5.7.1. Upper and lower price of the game
5.7.2. Reducing a matrix game to a linear programming problem
5.7.3. Selecting the optimal product range
5.8. Risks associated with the work of a sewing enterprise
Chapter 6. MAKING AN OPTIMAL DECISION IN CONDITIONS OF ECONOMIC RISK
6.1. Probabilistic formulation of preferential decisions
6.2. Assessing the degree of risk under conditions of certainty
6.3. Choosing the optimal number of jobs in a hairdressing salon, taking into account the risk of service
6.4. Statistical methods for decision making under risk conditions
6.5. Selecting the optimal plan using the method of constructing event trees
6.5.1. Decision tree
6.5.2. Optimizing your go-to-market strategy
6.5.3. Maximizing profits from stocks
6.5.4. Selection of the optimal project for the reconstruction of a dry cleaning factory
6.6. Comparative assessment of solution options
6.6.1. Choice optimal option solutions using statistical estimates
6.6.2. Normal distribution
6.6.3. Risk curve
6.6.4. Selecting the optimal solution using confidence intervals
6.6.5. Production cost forecasting model
6.7. The emergence of risks when setting the mission of the company's goals
6.8. Activities of service enterprises under risk conditions
6.8.1. Decoration and design company Enterprise for baking bakery products and their subsequent sale
6.8.3. Beauty saloon
Chapter 7. MANAGEMENT OF INVESTMENT PROJECTS UNDER CONDITIONS OF RISK
7.1. Investment projects in conditions of uncertainty and risk
7.1.1. Basic concepts of investment projects
7.1.2. Analysis and evaluation of investment projects
7.1.3. Risks of investment projects
7.2. Optimal choice volume of investment, ensuring maximum increase in output
7.3. Investments in a portfolio of securities
7.3.1. Investment management process
7.3.2. Diversified portfolio
7.3.3. Risks associated with investing in a securities portfolio
7.3.4. Practical recommendations on the formation of an investment portfolio
7.4. Analysis of the economic efficiency of an investment project
7.4.1. Analysis of associated risk factors
7.4.2. Preliminary estimate and selection of enterprises
7.4.3. Assessment of the financial condition of an enterprise as an investment object
7.4.4. Examples of analysis using financial ratios
7.4.5. Assessing the development prospects of the organization
7.4.6. Comparative financial analysis of investment projects
7.4.7. Analysis of organization survey methods on site
7.5. Taking risk into account in investment projects
7.5.1. Project Risk Assessment Model
7.5.2. Taking risk into account when investing
7.5.3. Practical conclusions on managing risky investment projects
Chapter 8. RISK MANAGEMENT OF TOURISM
8.1. Factors influencing the dynamics of tourism development
8.1.1. Development of tourism in Russia
8.1.2. Types and forms of tourism
8.1.3. Features of tourism - as factors of development uncertainty
8.2. Psychology of the impact of tourism on participants and others
8.2.1. Travel motivation
8.2.2. Impact of tourism
8.3. Risks associated with tourism activities
8.3.1. Factors affecting tourism and tourism economics
8.3.2. Classification of tourism risks
8.4. Economic Impact of Tourism
8.5. Making a management decision
8.6. Analysis of the activities of an organization providing tourism services under risk conditions
Chapter 9 RISK MANAGEMENT OF HOTELS AND RESTAURANTS
9.1. Development of hotel enterprises
9.2. Factors in the development of the restaurant business
9.3. Features and specifics of hospitality
9.4. Risks inherent in the hospitality industry and their management
9.4.1. Risk identification
9.4.2. Risks of investment projects
9.4.3. Reducing Risks in the Hospitality Industry
9.5. Management decisions in the hospitality business
Chapter 10. BASIC METHODS AND WAYS FOR REDUCING ECONOMIC RISKS
10.1. General principles risk management
10.1.1. Risk management process diagram
10.1.2. Examples of risks
10.1.3. Selecting Risk Management Techniques
10.2. Diversification
10.3. Risk insurance
10.3.1. The essence of insurance
10.3.2. Main characteristics of insurance contracts
10.3.3. Calculation of insurance transactions
10.3.4. Insurance contract
10.3.5. Advantages and disadvantages of insurance
10.4. Hedging
10.4.1. Risk Management Strategies
10.4.2. Basic Concepts
10.4.3. Forward and futures contracts
10.4.4. Exchange rate hedging
10.4.5. Main aspects of risk
10.4.6. Exchange rate hedging using swap
10.4.7. Options
10.4.8. Insurance or hedging
10.4.9. Cash flow synchronization
10.4.10. Hedging model
10.4.11. Measuring Hedging Effectiveness
10.4.12. Minimizing hedging costs
10.4.13. Correlated hedging transaction
10.5. Limitation
10.6. Reservation of funds (self-insurance)
10.7. Quality risk management
10.8. Purchasing additional information
10.9. Assessing the effectiveness of risk management methods
10.9.1. Risk financing
10.9.2. Assessing the effectiveness of risk management
Chapter 11. PSYCHOLOGY OF BEHAVIOR AND ASSESSMENT OF THE DECISION MAKER
11.1. Personal factors influencing the degree of risk when making management decisions
11.1.1. Psychological problems behavior of an economic personality
11.1.2. Management actions of an entrepreneur in the service sector
11.1.3. Personal attitude towards risk
11.1.4. Intuition and risk
11.2. Expected utility theory
11.2.1. Utility Function Graphs
11.2.2. Expected utility theory
11.2.3. Taking into account the decision maker's attitude towards risk
11.2.4. Group decision making
11.3. Theory of rational behavior
11.3.1. Prospect theory
11.3.2. Rational approach to decision making
11.3.3. Asymmetry of decision making
11.3.4. Behavior invariance
11.3.5. The role of information in decision making
11.4. Conflict situations
11.5. The role of the manager in making risky decisions
11.5.1. Decision making under risk conditions
11.5.2. Requirements for the decision maker
11.5.3. Principles for assessing the effectiveness of decisions made by decision makers
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Description : The textbook “Risk Theory and Modeling of Risk Situations” was written in accordance with the requirements of the 2nd generation State Educational Standards of the Ministry of Education Russian Federation. It corresponds to the programs of the disciplines “Risk Theory and Modeling of Risk Situations” and “Mathematical Methods of Financial Analysis” special. 061800 “Mathematical methods in economics”, discipline program “Decision Theory and Risk Management in the Financial and Tax Sphere” special. 351200 “Taxes and Taxation”, discipline program “Management” special. 061100 “Management”, as well as a number of economic specialties containing the discipline “Management”, since “Risk Management” is part of this discipline.
The textbook “Risk Theory and Modeling of Risk Situations” contains eleven chapters.
The first chapter, “The Place and Role of Economic Risks in Managing the Activities of Organizations,” gives a definition of an organization, examines the types of organizations, their characteristics and goals. The place and role of risks in economic activity is determined, the definitions and essence of risks are given. A classification of uncertainties and risks is given, the risk management system is revealed, and the basic concepts of risk management are given. The main mathematical methods for assessing economic risks are considered and their characteristics are given.
The second chapter, “Risks of service enterprises,” is devoted to service technologies and their differences from industrial technologies. A classification of risks of service sector enterprises is given and a dynamic analysis of the situation in the services market is given. A risk management model for service organizations is proposed.
The third chapter, “The influence of the main factors of market equilibrium on risk management,” is devoted to the study of the influence on changes in the degree of economic risk of such factors characterizing uncertainty market economy, such as: limiting risks, uncertainty of supply and demand, time accounting, elasticity, taxation, etc.
In the fourth chapter “Financial risk management”, theoretical basis financial risk management based on methods of financial and actuarial mathematics. A classification of financial risks is presented, the main parameters inherent in the considered financial risks, and using the proposed mathematical methods, analytical dependencies for their evaluation are given. This allows you to conduct a comparative quantitative analysis of risks and, on its basis, select the risk management methods that are the most effective.
In the fifth chapter " Quantitative assessments economic risk under conditions of uncertainty” discusses methods for making effective decisions under conditions of uncertainty, using various performance criteria. Multicriteria problems of choosing effective solutions are studied. We consider a sewing enterprise for which the optimal production volume is selected under conditions of uncertainty and the functioning of the enterprise in a risky situation is examined.
The sixth chapter, “Making an optimal decision under risk conditions,” is devoted to the presentation of probabilistic and statistical methods for making effective decisions and choosing the optimal solution using confidence intervals. The problem of choosing the optimal number of jobs in a hairdressing salon is considered, taking into account the risk of service. Using the “decision tree” method, the problems of optimizing the market entry strategy, maximizing profits from shares and choosing the optimal project for the reconstruction of a dry cleaning factory are considered. The material on the emergence of risks when setting the mission and goals of the company will be touched upon. The activities of a company for the decoration and design of premises, an enterprise for baking bakery products and their subsequent sale, and a beauty salon under risk conditions are investigated.
The seventh chapter, “Management of investment projects under conditions of risk,” provides the basic concepts of investment projects, their analysis and evaluation, and provides investment risks. Investigates investments in a portfolio of securities, the purpose of which is to form an effective portfolio made up of a combination of risk-free and risky assets. Methods for analyzing the economic efficiency of an investment project and comparative financial analysis of investment projects are given. The methodology for taking into account project risks is considered and practical recommendations for their management are provided.
The eighth chapter “Tourism Risk Management” is devoted to the types and forms, dynamics of tourism development in Russia. The factors of uncertainty in the development of tourism and the risks associated with tourism activities, as well as their classification, are considered. The economic impact of tourism and the specifics of making management decisions are studied. An analysis is given of the activities of the organization providing tourism services under risk conditions.
The ninth chapter, “Risk Management of Hotels and Restaurants,” examines development factors, features and specifics of hospitality, risks inherent in the hospitality industry, and their management. Recommendations are given for reducing and managing risks in the hospitality business.
In the tenth chapter, “Basic methods and ways to reduce economic” risks, economic tools for reducing risks are studied on the basis of mathematical modeling: diversification, insurance, hedging using forward and futures contracts, swaps and options, etc., and also summarizes methods for improving risk management aimed at to reduce their level and increase profitability. The effectiveness of risk management methods is assessed.
Chapter eleven “Psychology of behavior and assessment of the decision maker” is devoted to the study and systematization of the influence of psychological factors on the problems of behavior of market participants and the formation of packages of recommendations for risk management and the selection of effective solutions. Are being considered conflict situations and the role of the manager in making risky decisions.
At the end of the textbook “Risk Theory and Modeling of Risk Situations” for each chapter there are questions for repetition and self-control.
Contents of the textbook

THE PLACE AND ROLE OF ECONOMIC RISKS IN MANAGING THE ACTIVITIES OF ORGANIZATIONS
1.1. Organizations, types of enterprises, their characteristics and goals
1.2. The place and role of risks in economic activity

• 1.2.1. Definition and essence of risks
• 1.2.2. Management of risks
• 1.2.3. Risk classification
• 1.2.4. System of uncertainties

• 1.3.1. Management activities
• 1.3.2. Risk management
• 1.3.3. Risk Management Process
• 1.3.4. Mathematical methods for assessing economic risks

• 3.2.1. The relationship between market equilibrium and commercial risk
• 3.2.2. The influence of market equilibrium factors on changes in commercial risk
• 3.2.3. Modeling the process of achieving equilibrium
• 3.2.4. The impact of changes in demand on the level of commercial risk
• 3.2.5. The impact of changes in supply on the degree of commercial risk
• 3.2.6. Constructing dependencies between demand and supply

• 4.1.1. Classification of financial risks
• 4.1.2. Relationship between financial and operating leverage and total risk
• 4.1.3. Development risks

• 4.2.1. Types of interest risks
• 4.2.2. Operations with interest
• 4.2.3. Average percentages
• 4.2.4. Variable interest rate
• 4.2.5. Interest rate risks
• 4.2.6. Interest rate risk of bonds

• 4.3.1. Equivalent streams
• 4.3.2. Payment flows

• 4.4.1. Investment risks
• 4.4.2. Return rates on risky assets
• 4.4.3. Net present value
• 4.4.4. Annuity and sinking fund
• 4.4.5. Investment Valuation
• 4.4.6. Risky investment payments
• 4.4.7. Time discounting

• 4.5.1. Factors contributing to credit risks
• 4.5.2. Credit risk analysis
• 4.5.3. Techniques for reducing credit risks
• 4.5.4. Loan payments
• 4.5.5. Accumulation and payment of interest on a consumer loan
• 4.5.6. Credit guarantees

• 4.7.1. Relationship between interest rate and inflation rate
• 4.7.2. Inflation premium
• 4.7.3. The influence of inflation on various processes to reduce inflation

• 4.8.1. Currency conversion and interest accrual
• 4.8.2. Exchange rates over time
• 4.8.3. Reducing currency risks

• 4.9.1. Exchange risks
• 4.9.2. Impact of default and tax risk
• 4.9.3. Maximizing asset value

• 5.2.1. Concept of playing with nature
• 5.2.2. Subject of game theory. Basic Concepts

• 5.3.1. Guaranteed result criterion
• 5.3.2. Optimism criterion
• 5.3.3. Pessimism criterion
• 5.3.4. Savage's minimax risk criterion
• 5.3.5. Hurwitz's generalized maximin (pessimism - optimism) criterion

• 5.5.1. Multicriteria problems
• 5 5 2. Pareto optimality
• 5.5.3. Selecting solutions in the presence of multicriteria alternatives

• 5.7.1. Upper and lower price of the game
• 5.7.2. Reducing a matrix game to a linear programming problem
• 5.7.3. Selecting the optimal product range

• 6.5.1. Decision tree
• 6.5.2. Optimizing your go-to-market strategy
• 6.5.3. Maximizing profits from stocks
• 6.5.4. Selection of the optimal project for the reconstruction of a dry cleaning factory

• 6.6.1. Selecting the optimal solution using statistical estimates
• 6.6.2. Normal distribution
• 6.6.3. Risk curve
• 6.6.4. Selecting the optimal solution using confidence intervals
• 6.6.5. Production cost forecasting model

• 6.8.1. Interior decoration and design company
• 6.8.2. An enterprise for baking bakery products and their subsequent sale
• 6.8.3. Beauty saloon

• 7.1.1. Basic concepts of investment projects
• 7.1.2. Analysis and evaluation of investment projects
• 7.1.3. Risks of investment projects

• 7.3.1. Investment management process
• 7.3.2. Diversified portfolio
• 7.3.3. Risks associated with investing in a securities portfolio
• 7.3.4. Practical recommendations for building an investment portfolio

• 7.4.1. Analysis of associated risk factors
• 7.4.2. Preliminary assessment and selection of enterprises
• 7.4.3. Assessment of the financial condition of an enterprise as an investment object
• 7.4.4. Examples of analysis using financial ratios
• 7.4.5. Assessing the development prospects of the organization
• 7.4.6. Comparative financial analysis of investment projects
• 7.4.7. Analysis of organization survey methods on site

• 7.5.1. Project Risk Assessment Model
• 7.5.2. Taking risk into account when investing
• 7.5.3. Practical conclusions on managing risky investment projects

• 8.1.1. Development of tourism in Russia
• 8.1.2. Types and forms of tourism
• 8.1.3. Features of tourism - as factors of development uncertainty

• 8.2.1. Travel motivation
• 8.2.2. Impact of tourism

• 8.3.1. Factors affecting tourism and tourism economics
• 8.3.2. Classification of tourism risks

• 9.4.1. Risk identification
• 9.4.2. Risks of investment projects
• 9.4.3. Reducing Risks in the Hospitality Industry

• 10.1.1. Risk management process diagram
• 10.1.2. Examples of risks
• 10.1.3. Selecting Risk Management Techniques

• 10.3.1. The essence of insurance
• 10.3.2. Main characteristics of insurance contracts
• 10.3.3. Calculation of insurance transactions
• 10.3.4. Insurance contract
• 10.3.5. Advantages and disadvantages of insurance

• 10.4.1. Risk Management Strategies
• 10.4.2. Basic Concepts
• 10.4.3. Forward and futures contracts
• 10.4.4. Exchange rate hedging
• 10.4.5. Main aspects of risk
• 10.4.6. Exchange rate hedging using swap
• 10.4.7. Options
• 10.4.8. Insurance or hedging
• 10.4.9. Cash flow synchronization
• 10.4.10. Hedging model
• 10.4.11. Measuring Hedging Effectiveness
• 10.4.12. Minimizing hedging costs
• 10.4.13. Correlated hedging transaction

• 10.9.1. Risk financing
• 10.9.2. Assessing the effectiveness of risk management

• 11.1.1. Psychological problems of economic personality behavior
• 11.1.2. Management actions of an entrepreneur in the service sector
• 11.1.3. Personal attitude towards risk
• 11.1.4. Intuition and risk

• 11.2.1. Utility Function Graphs
• 11.2.2. Expected utility theory
• 11.2.3. Taking into account the decision maker's attitude towards risk
• 11.2.4. Group decision making

• 11.3.1. Prospect theory
• 11.3.2. Rational approach to decision making
• 11.3.3. Asymmetry of decision making
• 11.3.4. Behavior invariance
• 11.3.5. The role of information in decision making

• 11.5.1. Decision making under risk conditions
• 11.5.2. Requirements for the decision maker
• 11.5.3. Principles for assessing the effectiveness of decisions made by decision makers