Journal of Econometrics

J.Econometrics 146 (2008) 44--58

A Gaussian Approximation Scheme for Computation of Option Prices in Stochastic Volatility Models

^a Ai-ru (Meg) Cheng
^b A. Ronald Gallant
^c Chuanshu Ji
^d Beom S. Lee

^aDepartment of Economics, University of California, Santa Cruz
^bFuqua School of Business, Duke University
^cDepartment of Statistics and Operations Research, University of North Carolina
^dDepartment of Statistics, George Mason University

Received xxxx; revised xxxx; accepted xxxx

Abstract

We consider European options on a price process that follows the log-linear stochastic volatility model. Two stochastic integrals in the option pricing formula are costly to compute. We derive a central limit theorem to approximate them. At parameter settings appropriate to foreign exchange data our formulas improve computation speed by a factor of 1000 over brute force Monte Carlo making MCMC statistical methods practicable. We provide estimates of model parameters from daily data on the Swiss Franc to Euro and Japanese Yen to Euro over the period 1999 to 2002.

JEL Classification: G12, G13, G15, C11, C13, C15, C63

Keyword(s): central limit theorem, option pricing, stochastic volatility, foreign exchange, Markov chain Monte Carlo