A Markov Chain Quasi-Monte Carlo Method for Bayesian Estimation of Stochastic Volatility Model

Abstract

In this paper, we propose a Markov Chain Quasi-Monte Carlo (MCQMC) approach for Bayesian estimation of a discrete-time version of the stochastic volatility (SV) model. The Bayesian approach represents a feasible way to estimate SV models. Under the conventional Bayesian estimation method for SV models, pseudo-random numbers are usually used. Here we develop an algorithm to construct the Markov chain using a quasi-Monte Carlo sequence, or a low discrepancy sequence. We conjecture that the quasi-Monte Carlo sequence gives more precise estimates of the parameters in the SV model. We demonstrate the proposed method and justify our conjecture using both simulated and real nancial returns data.

Keywords: Stochastic Volatility, Bayesian Method, Markov Chain Quasi-Monte Carlo Method, Low Discrepancy Sequences, High-Dimensional Integrals, Deterministic Error Bound

JEL Classification: C11, C13, C22, C51