The Application Of Timevarying Copula And Extreme Value Copula In The Security Market Risk Measurement

Financial risk management is a kind of aggregate management, which always includes risk identify, risk measurement, risk management implement and risk control. Risk measurement is the key step during the financial risk management process. Statistic theory and quantitative method are used to measure the risk which may lead loss of financial asset. The risk measurement will provide quantitative base for the decision and practice of risk management.Market risk is the most common one in all kinds of risk for human financial activity. Value at Risk has become the standard risk measure for market risk in the practice and research. It is widely used in financial risk management field because of its convenience and simplicity. Despite had many advantages; VaR is not a kind of coherent measurement of risk and does not always satisfy the sub.additive which may not diversify the portfolio's risk. Artzner et al.(1997,1999) approach a coherent risk measure to overcome the shortfall of VaR. As a coherent measure of risk, Expected Shortfall will be a perfect risk measure for complementarity of VaR.Another problem in financial risk management is the description of dependence structure between different financial assets. In the past decades, the researches on dependence were always the hotspot and difficult point in finance and insurance. There are many shortfalls of assumptions and statistic in linear correlation, which made many difficulties in the dependence measurement of the different financial assets. Since the copula functions are applied into the quantitative risk management, the dependence researches among financial assets come into a new era.On learning and referencing the domestic and foreign researches of related field, we do research on the joint distribution between Shanghai and Hong Kong stock markets'indices'returns with several Copulas. We make Monte Carlo simulation, which dependence structure controlled by time varying parameters Copulas and extreme value Copulas, to measure the risk of the portfolio by VaR and Expected Shortfall. The research in the paper is innovative for market risk measurement and it has meaningful for practice of Copulas in China financial markets.There are six chapters in the paper:In the first chapter, we summarize the basic concepts on risk management and review the history of risk management. Then the categories of financial risk and their characteristic are approached. The techniques of the financial risk measurement are in the last of the chapter.Chapter 2 is the literature reviews. The first section is the literature reviews of VaR and Expected Shortfall. The second part of the chapter is the literature reviews on Copulas'application in financial risk management. The last section is the literature reviews on extreme value theory in financial risk management.Chapter 3 is the empirical research of the VaR and Expected Shortfall. The first two sections of the chapter is the definitions of the VaR and Expected Shortfall. In the last part of Chapter 3 we measure the market risk of Shanghai and Hong Kong stock markets by VaR and ES, respectively.Chapter 4 is the empirical research of risk measurement by Copulas. The basic concepts of copulas are in the first part of the chapter. Second section of the chapter is about the concept of dependence which including linear correlation, rank correlation and tail dependence. We use five Copulas to measure the portfolios'market risk between Shanghai and Hong Kong stock markets by Monte Carlo simulations.In Chapter 5 we approach the time varying dependence problem by two scatters of Shanghai and HK stock indices'returns. By fixing the width of the time window, we construct the time varying parameter Copula. We use Gaussian time varying Copula and Gumbel time varying Copula to measure the portfolio's risk between the two stock markets by VaR and ES.The last chapter is the market risk measurement by the extreme value theory and Copulas. The univariate extreme value theory and multivariate theory with Copula introductions are in the first two parts of the Chapter 6. In the last part of the chapter we construct extreme value Copula model to compute the probability of the joint extreme events between Shanghai and Hong Kong stock market. We also use extreme value Copula model to simulate the portfolio risk at different weight of two markets.We get some conclusions as below:(1)It is always known that t distribution model should be more risk than the Gaussian distribution model. However the empirical results of our paper showed that when we measure risk at a confidence level such as 95% and 97.5%, the Gaussian distribution appears to be at least risky as the t model; only above a confidence level at 99% does the higher risk in the tails of t distribution become apparent. On the other hand, in the risk measure of Expected Shortfall, the unusual condition does not exit. We could infer from our empirical results that Expected Shortfall is more suitable as a measure of risk than VaR and the stock market in China 2008 is more volatility than Hong Kong stock market.(2) We use three methods to estimate the parameters of the Copulas and make Monte Carlo simulation with Copulas to measure the portfolio's risk. The results show that Gumbel Copula is better than the other Copula in model the dependence structures between Shanghai and HK stock markets.(3) The dependence structures between Shanghai and Hang Seng indices vary when the time changes. We approach time vary parameter Copulas to model the changing dependence structure between the two markets. Compared the empirical results Chapter 5 and Chapter 4, the risk measurements estimated by time varying Copula get better than the stable Copulas.(4) We combine the Generalized Pareto distribution and Copula to model the joint extreme event between two stock markets, the probability of two markets'returns both below their 99% quantile is 0.000236 which is a twenty year event. We also measure the portfolios'risk at different weights by time varying Copula simulation. The results showed that the equal weights of portfolio will get lower risk and we could decrease the risk by adjust the weights following our results.We make some innovation researches in the paper:(1) In the market risk measurement, we use VaR and ES to measure the market risk of Shanghai and HK stock markets. We check out the shortfall of VaR in the risk measurement and prove that ES is more suitable as a risk measure.(2) We use five different kinds of Copulas to model the dependence structure between Shanghai and HK stock market and measure the risk of portfolio by Monte Carlo simulation.(3) By fixing the width of the time window, we analysis the time varying dependence structure by time varying Copulas and measure the risk of portfolio by the time varying Copulas.(4) We successfully combine the extreme value theory and the Copulas. We use extreme value Copula to compute the joint extreme events probability of the two markets and measure the portfolio's risk at different weights.