VaR Model Based on Fat-Tail Distribution of Extreme Value Theory with Its Application in Chinese Foreign Exchange Market

Abstract

In this paper, we study the statistical features of Chinese foreign exchange market data. Furthermore, we mainly fit the sample tail data employed Generalized Pareto Distribution (GPD), when building VaR model based on Fat-tail Distribution of Extreme Value Theory (EVT), we show that the model can be appropriate to be applied to Chinese foreign exchange market data. We have also proposed a procedure to better estimate the parameters in the GPD. Risk management is a broad concept involving various perspective. From the mathematical perspective considered, risk management is a procedure for shaping a loss distribution (for instance, an investor's risk profile). Among vast risk measurement models in past ten years, only a few have been widely accepted by practitioners, despite their active advantages in this area. Value-at-Risk (VaR), firstly developed by J.P.Morgan Bank in 1998, has become the stand measure that is uesd by financial analysts to quantify market risk. It is defined as the minimum potential loss in value of a portfolio of financial instruments with a given probability over a certain horizon. In another words, it is a number that indicates how much a financial institution could lose with probability θ over a given time horizon. From a statistical point of view, the estimation of VaR is actually the estimation of a quantile of the distribution of returns, which again is essentially related to the tail behavior of the return distribution. Traditional approaches often assume that log-return follows normal distribution, but many empirical studies have denied this assumption. Many researches find that the log-return of financial data has fatter tails than the normal distribution, and the normal assumption of return distribution may very likely result in underestimation of the market risk. Therefore, investigating the tail behavior and determining the accurate probability behavior of the return distribution at its tail part are of top importance in the risk management in the financial market. The main object of this paper is to conduct a comprehensive study of the above statistical features of the Chinese foreign exchange market and then present an appropriate VaR model for measuring the market risk. Encouraged by many successful applications of extreme value theory and Generalized Pareto Distribution, we shall then mainly use these two tools to carry out our study. We will find out whether or not the VaR model based on extreme value theory is an appropriate risk measurement tool in the Chinese foreign exchange market data.