An experimental comparison of Value at Risk estimates based on elliptical and hierarchical Archimedean copulas

In this paper, we estimate Value at Risk for a selected portfolio using elliptical and hierarchical Archimedean copulas, where the latter is based on a recent approach to estimation of hierarchical Archimedean copulas based on the Kendall correlation matrix. The estimates are compared using the Kupiec's test for three periods of time: a period of significant movements of index prices, a period of relative calm in the stock market and a long term period which includes the both situation in the stock market. Our experimental results show that the estimates based on elliptical copulas are more accurate in the periods of relative calm in the stock market, whereas the estimates based on hierarchical Archimedean copulas are more accurate in the period of significant movements in the stock market.