Measurements And Application Of The Extreme Risk Of Financial Data

The traditional technologies and methods of financial risk management, assetallocation and arbitrage strategies are all based on the Gaussian normal distributionassumption. Extreme financial risks rarely occur. But once it happens, it will bring ustremendous impact. Especially, into the1970s, significant fluctuations take place in thefinancial market, high volatility becomes routine. So the Gaussian normal distributionassumption goes under suspicion. Systemic study of the tail features of return-on-assetsof stocks generated from the theories above. It is quite necessary for both theoreticalresearch and practical application to study how to describe the tail features, how to fitits distribution, and how to get the estimations of the parameters related. This paperaims at the in-depth study and research of risk measures which are based on the extremevalue theory and compound extreme value models. This article mainly contents thefollowing knowledge:The paper does some systematic descriptions and analysis of two extremetheoretical models (BMM model and POT model) with their ideologies, theoreticalbasis and methods, then makes some analysis and comparion to their advantages anddisadvantages. Focused on the widely used generalized extreme value model, this articalpresents the concept and specifically describes three types, studies their maximumattraction domain; discusses the theoretical basis of generalized Pareto distribution,analyses how to determine the parameters and how to calculate the return on financialassets of the VaR and ES values. This paper also focuses on the criteria for selecting thethreshold in POT model with detailed description of three methods to determine thethreshold value; also analyses how to determine the parameters of the generalizedPareto distribution and calculate the return on financial assets of the VaR and ES values.With the basic knowledge of the Poisson-Gumbel compound extreme model, thepaper combines the GPD with the Poisson distribution, and defines new meaning to thevariables to get a new distribution named Poisson-GP compound over-thresholddistribution, discusses and compares with the three methods of the parameter estimation,which are maximum likelihood method, composite moment method and probabilityright moment method, the results show that the maximum likelihood method worksbest.With the GPD model and the Poisson-GP complex over-threshold distribution, the artical then presents an empirical analysis to the Shanghai Composite Index between1996-2013daily returns series. The results show that the two models both have verygood effect and high accuracy to fit the return on assets in financial market, and theycan reflect the data’s heavy tail features as well. Finally, we summarize the defects ofthis thesis and put forward the research directions in the future.