Value-at-Risk Based On Extreme Value Theory

As a financial market risk measurement, VaR (Value-at-Risk) appeared at the early part of 1990's. The risk management technique about VaR is a statistical model and method used to estimate and measure finance market risk. The correct estimates of VaR and CVaR are the real challenges to risk managers. The normal distribution is very often inadequate for the description of real financial data with heavy-tail distributions, especially very large quantile that interest to a risk manager. Extreme Value Theory models the tail of the return distribution rather than the whole distribution. It can capture the tail risk that often causes large losses in financing institutions, so it is a good approach for risk measurement in finance field.Extreme Value Theory is used to analysis the extreme values of random vectors and processes by the statistic methods. The classic extreme value theory requests that series is independent and has identical distribution. This paper introduces the extremal index under the assumption that the series is stationary, builds a POT model by using the method of declustering, and then calculates the estimates of VaR and CVaR.In this article, I introduce the knowledge about financial risk, look back the development of the technology of risk measurement, sum up the present situation about domestic and foreign VaR research, and introduce the concept and computing theorem in detail, synthetically compare all these computing methods, and analyze the advantages and the disadvantages as the model of mathematical statistical model. Then I analyze CVaR which be derived from VaR and approach more closely to the real feeling of investors. Following,I research the VaR and CVaR of JPY/USD foreign exchange rate, the result proved that the accurate for the estimations have been improved by introducing the extremal index. In order to expose more exactly of the market risk faced by financing institutions, and manage risk more deeply and completely, This article expands research in the following aspects: multivariate abnormal distribution family, the measurement of correlation function in the portfolio selection and Copula function.This article aims at improving the applicability and precision of VaR by using the knowledge of Extreme value theory and etc.. I believe that this article is instructive for our financial institutions to control market risk.