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Analytic Approximations for Spread Options


  • Carol Alexander

    () (ICMA Centre, University of Reading)

  • Aanand Venkatramanan

    () (ICMA Centre, University of Reading)


This paper expresses the price of a spread option as the sum of the prices of two compound options. One compound option is to exchange vanilla call options on the two underlying assets and the other is to exchange the corresponding put options. This way we derive a new analytic approximation for the price of a European spread option, and a corresponding approximation for each of its price, volatilty and correlation hedge ratios. Our approach has many advantages over existing analytic approximations, which have limited validity and an indeterminacy that renders them of little practical use. The compound exchange option approximation for European spread options is then extended to American spread options on assets that pay dividends or incur carry costs. Simulations quantify the accuracy of our approach; we also present an empirical application, to the American crack spread options that are traded on NYMEX. For illustration, we compare our results with those obtained using the approximation attributed to Kirk (1996) which is commonly used by traders.

Suggested Citation

  • Carol Alexander & Aanand Venkatramanan, 2007. "Analytic Approximations for Spread Options," ICMA Centre Discussion Papers in Finance icma-dp2009-06, Henley Business School, Reading University, revised Jun 2009.
  • Handle: RePEc:rdg:icmadp:icma-dp2009-06

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    References listed on IDEAS

    1. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
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    Cited by:

    1. Tomáš Václavík & Andrea Klimešová, 2016. "Gas Swing Options: Introduction and Pricing using Monte Carlo Methods," Acta Oeconomica Pragensia, University of Economics, Prague, vol. 2016(1), pages 15-32.
    2. Emmanuel Hanert & Aanand Venkatramanan, 2008. "Meshfree Approximation for Multi-Asset Options," ICMA Centre Discussion Papers in Finance icma-dp2009-07, Henley Business School, Reading University, revised Jun 2009.

    More about this item


    Spread options; exchange options; American options; analytic formula; Kirks approximation; correlation skew;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General


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