The valuation of European options when asset returns are autocorrelated

Szu‐Lang Liao and Chao‐Chun Chen

Journal of Futures Markets, 2006, vol. 26, issue 1, 85-102

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. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:85–102, 2006

Date: 2006
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