对金融过程的波动性进行建模

A. D. Kozhukhivsʹkyy
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引用次数: 0

摘要

风险管理的任务在人的实际活动的所有分支中都有体现。特别是银行业、保险、投资公司的数学建模、估计和预测风险(以可能损失的水平及其概率为特征)的主题问题。在激烈竞争和变化的条件下经营的制造企业,以及从事其他类型活动的企业。对于今天可能的损失的数学描述,有一套思想上不同的方法,这些方法是基于经典的统计方法和智能数据分析方法。因此,为了评估市场和一些其他类型的风险,使用了风险价值(VaR)技术的各种变体,这使得有可能获得实际使用的可接受的质量结果。在信用风险评估中发现,在分类类型的基础上运用了逻辑回归、线性回归、参考向量法(MOV)、判别分析、模糊逻辑、神经模糊模型、贝叶斯数据分析和决策树等方法,以及这些方法的组合。对保险中的金融风险进行评估,除了上述方法外,还运用了随机变量分布理论、广义线性模型、回归分析(线性模型和非线性模型)、贝叶斯网络等模型和方法。所创建的计算机系统使根据历史建模和蒙特卡罗方法估计VaR可能损失的值成为可能。要解决这个问题,必须首先获得相关金融异方差过程的波动率预测的估计。为了计算波动率预测的估计,通常使用具有条件异方差的广义自攻击模型(UARUG或GARCH)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Modeling the volatility of financial processes
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.
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