Title: Computing value-at-risk via peaks-over-threshold generalized Pareto distribution
Authors: Yi He - University of Amsterdam (Netherlands) [presenting]
Liang Peng - Georgia State University (United States)
Abstract: The value-at-risk of financial loss in the tail is computed by fitting a generalized Pareto distribution to exceedance over a high but not divergent threshold. Such a model is inferred for both independent observations and time series data. We show that asymptotic variance for the maximal likelihood estimator depends on the choice of threshold, the tail index of the distribution, and the parameters of time-series model, which all make it quite challenging to quantify the uncertainty of high-level value-at-risk measure. To make the inference practically feasible, we then propose a smooth empirical likelihood based method for constructing a confidence interval for the value-at-risk based on either independent errors or AR-GARCH errors. The finite sample performance of the derived confidence intervals is demonstrated through numerical studies before applying to real data.