A New Approach to Importance Sampling in Taylor’s Stochastic Volatility Model

Abstract

This article presents the general analysis of finite high-dimensional integrals using the Importance Sampling (IS) in aim to the parameter estimation of Taylor’s stochastic volatility (SV) model. After we proceed to make an alternative derivation for Sequential Importance Sampling (SIS) in previous literatures, we propose a new approach to select the optimal parameters of sampler, which is called as Universal Importance Sampling (UIS). UIS minimizes the Monte Carlo variance and numerically performs at least the same accurately as the SIS algorithm, but the computational efficiency get greatly improved. We apply both methods and investigate the SV model on the data, then make comparisons of the results.

KEYWORDS:

• Importance sampling
• Monte Carlo
• Stochastic volatility

Mathematical Subject Classification:

• C15
• C22
• C52
• 62
• 91