A dynamic method-of-moments copula model approach for market risk estimates

Wolfgang Aussenegg and Christian Cech

Abstract

This study presents a method-of-moments copula approach in a dynamic setting for estimating the market risk of asset portfolios. On using exponential generalized conditional heteroscedasticity (EGARCH) volatility-adjusted returns to account for heteroscedasticity, our findings reveal that the method-of-moments approach significantly reduces the copula estimation time for 99% value-at-risk estimates without loss of accuracy while outperforming several benchmark models. This creates an advantage for practical applications, especially for portfolios with higher dimensions. We also use this model to calculate 97.5% expected shortfall estimates. Our empirical results are based on a mixed 21-dimensional portfolio consisting of five classes of financial assets often included in trading books of financial institutions (stocks, stock indexes, bonds, foreign exchange and commodities). An investigation period of nearly 35 years (January 1990 to November 2024) ensures the inclusion of several severe crisis periods with strong sudden price movements and corresponding shocks to the dependence structure. More than 8200 trading days and a rolling 250-day estimation window for dynamic out-of-sample risk estimates generate an interesting base for accuracy tests. Overall, the best accuracy is generated by a meta-Student t model using EGARCH volatility-adjusted returns with method-of-moments copula estimation. An additional simulation study shows that the computational advantage of our dynamic method-of-moments copula approach persists for portfolios of higher dimensions with up to 400 risk factors.