Semi-parametric Method for Estimating Tail Related Risk Measures in the Stock Market

The generalized Pareto distribution (GPD) approach for estimating the Value-at-Risk (VaR) and the expected shortfall (ES) is compared to other methods for evaluating extreme risk with normally distributed returns. When the market index returns have a fat-tailed distribution, the risk measures computed from the normal distribution underestimate the tail-related risk. We also compare the computation results of the VaR based on the GPD approximations to those based on the RiskMetrics methodology and GARCH model estimation. The estimates of the VaR are robust to a variety of threshold values. Contrary to this, the VaR values based on the RiskMetrics methodology and the GARCH model are extremely volatile. From a risk manager's perspective, it would be difficult to adjust capital requirement of a financial institution to conditional market risk. Due to concerns raised for practical and statistical reasons, we can conclude that the GPD method for measuring unconditional market risk is more appropriate for measuring and managing the tail-related risk.