Estimating Extreme Correlation for the EVT-Type VaR-A Copula Approach

Abstract

In this paper we propose to use the Clayton copula to derive a time-varying correlation model for calculating the extreme value theory (EVT) type Value at Risk (VaR). The EVT is most useful in estimating tail probabilities of extreme events. Therefore, it does not rely on the normality assumption of financial asset returns as often assumed by the common methodologies for calculating VaR. However, most calculations of the EVT-type VaR are based on constant correlation models. Since correlation coefficients tend to change over time, especially under severe market shocks, the constant correlation models could lead to incorrect correlation representations. The time-varying correlation matrix derived by the Clayton copula captures the correlation of extreme events. Theoretically, the resulting VaR should be a better risk measure than those calculated by constant correlation models. This approach also has the merit of dealing with the problem of insufficient samples when estimating extreme correlation. We construct nine portfolios to compare the performance of the EVT-type VaR calculated by the proposed correlation model with that calculated by a constant correlation model. The portfolios are constructed with various weights in equity and fixed-income assets that are exposed to four market risk factors. Using a historical VaR as benchmark, the results show that on average, the new approach outperforms that with constant correlation, especially in portfolios with less risk exposure to the NTD/USD foreign exchange rate.