《a new algorithm based on copulas for var valuation with empirical calculations》.pdf

Theoretical Computer Science 378 (2007) 190–197 /locate/tcs A new algorithm based on copulas for VaR valuation with empirical calculations Gang Chenga,b , Ping Lic,b,∗, Peng Shid a Wuhan University, Wuhan 430070, PR China b City University of Hong Kong, Kowloon, Hong Kong c Beihang University, Beijing 100083, PR China d University of Wisconsin-Madison, Madison, WI 53706, USA Abstract This paper concerns the application of copula functions in VaR valuation. The copula function is used to model the dependence structure of multivariate assets. After the introduction of the traditional Monte Carlo simulation method and the pure copula method we present a new algorithm based on mixture copula functions and the dependence measure, Spearman’s rho. This new method is used to simulate daily returns of two stock market indices in China, Shanghai Stock Composite Index and Shenzhen Stock Composite Index, and then empirically calculate six risk measures including VaR and conditional VaR. The results are compared with those derived from the traditional Monte Carlo method and the pure copula method. From the comparison we show that the dependence structure between asset returns plays a more important role in valuating risk measures comparing with the form of marginal distributions. c 2007 Elsevier B.V. All rights reserved. Keywords: Value-at-Risk; Copulas; Spearman’s rho; Monte Carlo simulation 1. Introduction This paper presents an algorithm using copula functions to simulate random variables and further to valuate the