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The valuation of European options when asset returns are autocorrelated
Author(s) -
Liao SzuLang,
Chen ChaoChun
Publication year - 2006
Publication title -
journal of futures markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.88
H-Index - 55
eISSN - 1096-9934
pISSN - 0270-7314
DOI - 10.1002/fut.20192
Subject(s) - black–scholes model , call option , econometrics , economics , stochastic volatility , autocorrelation , geometric brownian motion , implied volatility , volatility (finance) , valuation (finance) , volatility smile , valuation of options , mathematics , financial economics , diffusion process , statistics , finance , economy , service (business)
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