Estimating quantile risk measures using extreme value theory in finance and insurance - Uyaco, Filame Joy Depakakibo
This paper discusses the modeling strategy of extreme value theory (EVT) to describe the behavior of financial returns and medical insurance claim losses. Using EVT, the modeling focuses on "block maxima" approach to fit the generalized extreme value distribution (GEV) and the "peak over threshold" approach to fit the generalized Pareto distribution (GPD). We use the maximum likelihood estimation (MLE) and method of probability-weighted moments (PWM) to estimate the parameters of GEV and GPD. Applying EVT, however, faces many challenges. This includes the scarcity of extreme data, determining whether the series is heavy-tailed, choosing the threshold and choosing the methods of estimating the parameters. This paper provides tools to address these issues. We shall apply the EVT concept to the estimation of quantile risk measures such as Value-at-Risk (VaR), Expected Shortfall (ES) and Return Level. We compare the estimates of quantile risk measures based on the parameter estimation techniques. Furthermore, we compare VaR and ES estimates using gaussian and general Pareto distribution-peak over threshold (with reference to MLE and PWM) models.