Non-Gaussian Bridge Sampling with an Application

Abstract

This paper provides a new bridge sampler that can efficiently generate sample paths, subject to some endpoint condition, for non-Gaussian dynamic models. This bridge sampler uses a companion pseudo-Gaussian bridge as the proposal and sequentially re-simulates sample paths via a sequence of tempered importance weights in a way bearing resemblance to the density-tempered sequential Monte Carlo method used in the Bayesian statistics literature. This bridge sampler is further accelerated by employing a novel idea of k-fold duplicating a base set of sample paths followed by support boosting. We implement this bridge sampler on a GARCH model estimated to the S&P 500 index series, and our implementation covers both parametric and non-parametric conditional distributions. Our performance study reveals that this new bridge sampler is far superior to either the simple-rejection method when it is applicable or other alternative samplers designed for paths with a fixed endpoint. Computing SRISK of the NYU-Stern Volatility Institute is then used to demonstrate the method's real-life applicability.

Keywords: sequential Monte Carlo, density tempering, Metropolis-Hastings, GARCH, systemic risk, infill estimation