Modeling the volatility of financial processes

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Tasks of risk management meet in all branches of practical activity of the person. Especially topical problems of mathematical modeling, estimation and forecasting of risks (which are characterized by the level of possible losses and their probability) is for the banking sector, insurance, investment companies. manufacturing enterprises operating in conditions of fierce competition and changing conditions, and for other types of activity. For the mathematical description of possible losses today there is a set of ideologically different approaches, which are based on classical statistical methods and methods of intelligent data analysis. Thus, to evaluate market and some other types of risks, various variants of the Value-at-Risk (VaR) technique are used, which makes it possible to obtain acceptable quality results for practical use.In the assessment of credit risks found the use of nonlinear models of classification type on the basis of logistical regression, linear regression, method of reference vectors (MOV), discriminatory analysis, fuzzy logic, neuro-fuzzy models, methods of Bayesian data analysis and decision tree, as well as combinations of these methods. To assess financial risks in insurance, the above-mentioned methods are used, as well as the theory of distributions of random variables, generalized linear models, regression analysis (linear and nonlinear models), Bayesian networks and other models and methods. The created computer system makes it possible to estimate the value of possible losses of VaR according to the methods of historical modeling and Monte Carlo. To solve this problem, you must first obtain estimates of the volatility forecasts of the relevant financial heteroscedatic processes. To calculate estimates of volatility forecasts, a model of generalized auto-aggression with conditional heteroscedasticity (UARUG or GARCH) is often used.