Archimedean copula in the computation of value-at-risk : an application to Singapore stock market.

Abstract

The Value-at-Risk (VaR) is of central importance in modern financial risk management. Of the various methods that exist to compute the VaR, the most popular are historical simulation, the variance-covariance method. Gaussian Copula approach is preferred over the conventional method to compute VaR because it shows a closer estimate to the actual VaR. However,Gaussian copula is ineffective in estimating VaR during extreme market conditions. In this study, we propose the use of Archimedean Copula instead of Gaussian Copula in estimating VaR under extreme market conditions. This hypothesis is drawn based on past studies showing that Archimedean Copula is able to take into account of upper or lower tail dependence unlike Gaussian Copula. The data analysis is based on historical stock data from two Singapore bluechip stocks namely Hong Leong Finance and Starhub in FY 2005-2007. The data will then undergo backtesting in extreme market conditions developed due to the subprime mortgage crisis in the U.S during FY 2008-2009. The findings show that Archimedean Copula gives a better estimate of VaR in terms of percentage change of portfolio return and the estimated distribution of returns for the portfolio in the extreme market condition.