The Calibration of Market Risk Measures During Period of Economic Downturn: Market Risks and Measures

Abstract

This study explores the calibration of market risk measures during period of economic downturn. This calibration is done in two frameworks: firstly individual profit and loss distribution is modelled using two different types of extreme value distribution namely: the generalized extreme value (GEV) distribution, and the generalized Pareto distribution (GPD). The resulting shape parameters are all positive indicating that these distributions can in fact capture the negative skewness and excess kurtosis of the profit and loss (P&L) distribution during period of economic downturn. We show that the presence of such positive shape parameters indicates the existence of large probabilities of extreme price drops in the left tail of the P&L distribution. Based on these results the second framework used in this study builds two multivariate copula distributions with GEV and GPD marginals. This procedure captures the dependence structure of stock markets during periods of financial crisis. To illustrate the computation of market risk measures; we consider one elliptical copula (student t copula) and one Archimedean copula (Gumbel copula). Using two stock market indices we compute what we refer to as EVT based mark risk measures and the copula based market risk measures for both the left and right tails of the P&L distribution. Our results suggest that copula based risk measures are more reliable in predicting the behavior of market risks during period of economic downturn.