Comparison of Risk Calculation Based on Historical Simulation and the Copula Function

Abstract

The fundamental aim of this paper is to compare risk calculation based on historical simulation with risk calculation based on the copula function. In the case of historical simulation it is assumed that future data can be estimated on the basis of historical data. The copula function is a multi-dimensional distribution function with which we can explore the correlations between probability variables (in this case, equities within the portfolio) and simulate or forecast their future development. A method is called “better” if it enables a more accurate estimation of risk, i.e. where actual and estimated values are closer to each other. In this paper, the Value at Risk and Expected Shortfall risk measures are used to determine risk, while the accuracy of the two simulations is tested with the backtesting method. Based on the results of the empirical study of the daily price data of seven equities we may conclude that risk calculation based on the copula function may contribute to a more precise modelling of risk.