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The valuation of European options when asset returns are autocorrelated

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  • Szu‐Lang Liao
  • Chao‐Chun Chen

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

Suggested Citation

  • Szu‐Lang Liao & Chao‐Chun Chen, 2006. "The valuation of European options when asset returns are autocorrelated," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(1), pages 85-102, January.
    • Handle: RePEc:wly:jfutmk:v:26:y:2006:i:1:p:85-102
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    Cited by:

    1. Abootaleb Shirvani & Svetlozar T. Rachev & Frank J. Fabozzi, 2019. "A Rational Finance Explanation of the Stock Predictability Puzzle," Papers 1911.02194, arXiv.org.
    2. Yu-Hong Liu & I-Ming Jiang & Shih-Cheng Lee & Yu-Ting Chen, 2011. "The Valuation Of Reset Options When Underlying Assets Are Autocorrelated," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 5(2), pages 95-114.
    3. Yang, Chih-Yuan & Jhang, Ling-Jhen & Chang, Chia-Chien, 2016. "Do investor sentiment, weather and catastrophe effects improve hedging performance? Evidence from the Taiwan options market," Pacific-Basin Finance Journal, Elsevier, vol. 37(C), pages 35-51.
    4. Wang, Chou-Wen & Wu, Chin-Wen & Tzang, Shyh-Weir, 2012. "Implementing option pricing models when asset returns follow an autoregressive moving average process," International Review of Economics & Finance, Elsevier, vol. 24(C), pages 8-25.
    5. Yang, Chih-Yuan & Chang, Chia-Chien, 2024. "Do economic uncertainty and persistence in housing prices matter on mortgage insurance?," The Quarterly Review of Economics and Finance, Elsevier, vol. 95(C), pages 33-44.

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