The Valuation of European Options When Asset Returns Are Autocorrelated

Abstract

This article derives the closed-form formula for a European option on an asset with returns following a continuous-time type of first-order moving average process, which is called an MA(1)-type option. The pricing formula of these options is similar to that of Black and Scholes, except for the total volatility input. Specifically, the total volatility input of MA(1)-type options is the conditional standard deviation of continuous-compounded returns over the option`s remaining life, whereas the total volatility input of Black and Scholes is indeed the diffusion coefficient of a geometric Brownian motion times the square root of an option`s time to maturity. Based on the result of numerical analyses, the impact of autocorrelation induced by the MA(1)-type process is significant to option values even when the autocorrelation between asset returns is weak.