Dissertation > Economic > Fiscal, monetary > Finance, banking > Finance, banking theory > Financial market

VaR and CVaR Estimator Based on Extreme Value Theory

Author ZhangLiuQing
Tutor YangShanChao
School Guangxi Normal University
Course Probability Theory and Mathematical Statistics
Keywords VaR CVaR Extreme Value Theory Dynamic risk model
CLC F830.9
Type Master's thesis
Year 2009
Downloads 81
Quotes 2
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Accompanied by increasingly severe volatility in financial markets, financial risk management has gradually become one of the the most important part of financial activities in recent years, VaR and CVaR two risk measurement tool has become widely accepted and applied them an accurate estimate risk management workers the biggest challenges facing this paper first introduces the VaR and CVaR theory as well as their common estimation methods, including variance - covariance method, historical simulation, Monte Carlo simulation, and describe the advantages of these methods and inadequate. CVaR is a coherent risk measure and has some very good mathematical properties, many scholars have launched a CVaR CVaR estimation method is still scarce and poor accuracy. main purpose of this paper is construct a new method have higher accuracy of the estimated CVaR Acerbi and Tasche (2002, [47]) pointed out that an integral representation of the ES and ES and CVaR in the continuous case are equivalent. In this paper, extreme value theory and the above theory, the CVaR of a new extreme POT estimation method a common method of CVaR order statistics method, this method is easy to understand, easy to calculate, will be used with extreme value method to compare this paper, we consider light-tailed distribution, heavy tail distribution, independent samples, dependent sample a variety of circumstances, the use of numerical simulation method Comparison of the proposed CVaR extreme value estimation methods and order statistics method excellent value The simulation results show that the method accuracy than traditional methods, is a very good method of this paper, another to build a dynamic risk management models, considering the volatility of time-varying volatility for the next time and the first time Volatility, throughout the period of time the volatility is constantly changing. static model does not consider the time-varying volatility, assuming that the volatility in the whole process is fixed. GARCH model can well reflect the volatility the process of change, which is widely used in the analysis of financial time series. detailed description of how to use the GARCH model and optimization method for building dynamic risk management models. Finally, we in the empirical analysis of dynamic risk management model is applied on the date of the Shanghai Composite Index the number of return series analysis we can see that the traditional static risk models can not measure the risk of volatility period, we introduce dynamic extreme risk management model still has a high degree of accuracy. Meanwhile, we will also establish residue poor distribution of the t-distribution, GED distribution skewed-t the skewed-GED distribution of the the GARCH APARCH model, through information criterion and Backtest find the most suitable model of the Shanghai Composite Index.

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