Tail Estimation And Extreme Value Measurement For Financial Market Risk

Classical Theories for risk measurement estimate loss CDF of asset portfolios by sample data of profit-loss series, then get the probable loss in a given confidential level. But in recent years, people found that CDF on the basis of loss data worked better in central area equivalent of high frequency and low loss data, but performed poorly in tails consisting of low frequency and high loss data. In general, just the extreme events in distribution's tails are able to cause catastrophic effect for quite a number of institution and individual investors because lacking effective prediction and adequate reserve fund of risks. So tail risk measurement has already been the crucial topic in the field of financial risks. This paper focuses on financial risks measurement and management on extreme values, and can provide some effective methods to theoretical investigation and empirical analysis. It is undoubtedly meaningful to risk identification and management when the influences of financial crisis still exist, financial market is also in the regulatory period, and the crisis in second round might be truth.Extreme value theory and stress testing are important analysis tools to extreme events, and had been involved in VaR model in recent years. People got some satisfactory results when used these two tools to tail risk measurement. But there are still some problems in applications of extreme model and stress testing. Researchers and practitioners of risk management are making great efforts to improve them. This paper discussed some problems which have major sense to model effectiveness. Such problems involved threshold selection, tail dependence of sample data and estimation of extremal index, risk measurement of coherent stress testing, etc. We got some satisfactory results. Meanwhile, on the basis of researches on risk measurement for asset portfolio, we also discussed topics of systematic risk management, from the standpoint of macro-prudential regulations, presented some suggestions.The main contents and conclusions are summarized as follows: the first chapter introduces theoretical and practical sense, present some research achievements about extreme value theory and stress testing, summarize contents, methods and innovations of this paper. The second chapter introduces foundations of extreme value theory such as research objects and Fisher-Tippett theorem, GEV and GPD model, estimation on shape parameter in GEV. The third chapter discusses threshold selection basing on change point theory. The forth chapter studies estimations on tail dependence and extremal index, calculates tail index of SHCI and S&P500, compares the results. Then we review blocks method, reciprocal cluster method, run method and Ferro-Segers method on extremal index calculations, and get results in all methods. Finally we present a new econometric way to get extremal index, and prove its effectiveness. The fifth chapter discusses risk measurement in a coherent stress testing framework, makes GPD be the specific distribution of stress testing, involved stress scenario in sample data, uses historical simulation, EGARCH(1,1)-M model in empirical test. The sixth chapter starts on reactions of major economic entities on the financial crisis, discusses systematic risk management in extreme conditions, analyzed principle and framework of macro-prudential regulation, and its difference and connection to micro-prudential regulation. We also give some advices.This paper is mainly for theory and supports by empirical analysis. Its key tools are quantitative researches, supplement by qualitative analyses. The primary innovations include as theoretical and practical sides.Theoretical innovations are as follows: presents a new method for threshold selection basing on change point theory; presents a econometric way to calculate extremal index, discusses principle of this method; introduce GPD as stress scenario distribution, constructs a coherent stress testing framework; discusses systematical risk management in extreme conditions, gives some advices about macro-prudential regulations.Empirical innovations are as follows: uses second-order difference method of threshold selection in VaR model, improves existing methods, and calculate SHCI's VaR in different confidence levels; compares the tail indexes between SHCI and S&P500; calculates the extremal indexes of SHCI and S&P500 by blocks method, reciprocal cluster method, run method and Ferro-Segers method, uses the results to VaR calculation; get extremal indexes of SHCI and S&P500 in econometric way, and this result is close to the original ones; apply EGARCH(1,1)-M model to estimate dynamic VaR and ES, the consequence shows that stress scenario has prominent influence to VaR estimation, in 95% level, dynamic VaR estimated by EGARCH(1,1)-M model can meet Kupiec test.