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The impact of return nonnormality on exchange options

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  • Minqiang Li

Abstract

The Margrabe formula is used extensively by theorists and practitioners not only on exchange options, but also on executive compensation schemes, real options, weather and commodity derivatives, etc. However, the crucial assumption of a bivariate normal distribution is not fully satisfied in almost all applications. The impact of nonnormality on exchange options is studied by using a bivariate Gram–Charlier approximation. For near‐the‐money exchange options, skewness and coskewness induce price corrections that are linear in moneyness, whereas kurtosis and cokurtosis induce quadratic price corrections. The nonnormality helps to explain the implied correlation smile observed in practice. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:845–870, 2008

Suggested Citation

  • Minqiang Li, 2008. "The impact of return nonnormality on exchange options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(9), pages 845-870, September.
    • Handle: RePEc:wly:jfutmk:v:28:y:2008:i:9:p:845-870
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    Cited by:

    1. Edward P. C. Kao & Weiwei Xie, 2017. "Pricing spread options by generalized bivariate edgeworth expansion," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-30, June.
    2. Oprea Otilia-Roxana, 2017. "The Effects Of The Economic Crisis On European Financial Integration And Economic Growth," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 4, pages 256-264, August.
    3. Karine Constant & Natacha Raffin, 2016. "Environnement, croissance et inégalités : le rôle particulier du canal de la santé," Revue française d'économie, Presses de Sciences-Po, vol. 0(3), pages 9-29.
    4. Minqiang Li & Kyuseok Lee, 2011. "An adaptive successive over-relaxation method for computing the Black-Scholes implied volatility," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1245-1269.
    5. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    6. Minqiang Li & Jieyun Zhou & Shi-Jie Deng, 2010. "Multi-asset spread option pricing and hedging," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 305-324.
    7. Karine Constant & Natacha Raffin, 2016. "Environnement, croissance et inégalités : le rôle particulier du canal de la santé," Revue française d'économie, Presses de Sciences-Po, vol. 0(3), pages 9-29.
    8. Kwangil Bae & Jangkoo Kang & Hwa‐Sung Kim, 2018. "Call options with concave payoffs: An application to executive stock options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(8), pages 943-957, August.
    9. Kwangil Bae, 2019. "Valuation and applications of compound basket options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(6), pages 704-720, June.

    More about this item

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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