A Recursive Bayesian Model for Extreme Values

Abstract

In this paper, we propose a new approach for analyzing extreme values such as large losses in financial markets. Our goal is to compute the predictive distribution of extreme events that are clustered in time. We apply a stochastic parametrization of the generalized extreme value distribution to model the asymptotic behavior of the block-maximum and derive a Rao-Blackwellized particle filter. This reduces the parameter space, and we derive a concise, recursive solution. Using the filter, the predictive distribution, conditioned on the past data, is computed at each sample-time. We introduce a new risk-measure, pVaRα, that is a more robust estimate of the true nature of value-at-risk, and illustrate our results using both simulated data and actual stock market returns from 1928-2017.