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The Impact of Return Nonnormality on Exchange Options

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  • Li, Minqiang

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 which are linear in moneyness, while kurtosis and cokurtosis induce quadratic price corrections. The nonnormality helps to explain the implied correlation smile observed in practice.

Suggested Citation

  • Li, Minqiang, 2007. "The Impact of Return Nonnormality on Exchange Options," MPRA Paper 7020, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:7020
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    File URL: https://mpra.ub.uni-muenchen.de/7020/1/MPRA_paper_7020.pdf
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    1. repec:wsi:ijfexx:v:04:y:2017:i:02n03:n:s2424786317500177 is not listed on IDEAS
    2. repec:cbu:jrnlec:y:2017:v:4:p:256-264 is not listed on IDEAS
    3. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    4. 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.
    5. 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.

    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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