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A general closed-form spread option pricing formula

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  • Caldana, Ruggero
  • Fusai, Gianluca

Abstract

We propose a new accurate method for pricing European spread options by extending the lower bound approximation of Bjerksund and Stensland (2011) beyond the classical Black–Scholes framework. This is possible via a procedure requiring a univariate Fourier inversion. In addition, we are also able to obtain a new tight upper bound. Our method provides also an exact closed form solution via Fourier inversion of the exchange option price, generalizing the Margrabe (1978) formula. The method is applicable to models in which the joint characteristic function of the underlying assets forming the spread is known analytically. We test the performance of these new pricing algorithms performing numerical experiments on different stochastic dynamic models.

Suggested Citation

  • Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
  • Handle: RePEc:eee:jbfina:v:37:y:2013:i:12:p:4893-4906
    DOI: 10.1016/j.jbankfin.2013.08.016
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Jing Li & Lingfei Li & Rafael Mendoza-Arriaga, 2016. "Additive subordination and its applications in finance," Finance and Stochastics, Springer, vol. 20(3), pages 589-634, July.
    2. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2014. "A general HJM framework for multiple yield curve modeling," Papers 1406.4301, arXiv.org, revised May 2015.
    3. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2014. "A general HJM framework for multiple yield curve modeling," Working Papers hal-01011752, HAL.
    4. Kenichiro Shiraya & Akihiko Takahashi, 2015. "Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models," CIRJE F-Series CIRJE-F-980, CIRJE, Faculty of Economics, University of Tokyo.
    5. Mesias Alfeus & Erik Schlögl, 2018. "On Numerical Methods for Spread Options," Research Paper Series 388, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Farkas, Walter & Gourier, Elise & Huitema, Robert & Necula, Ciprian, 2017. "A two-factor cointegrated commodity price model with an application to spread option pricing," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 249-268.
    7. Shiraya, Kenichiro & Takahashi, Akihiko, 2017. "A general control variate method for multi-dimensional SDEs: An application to multi-asset options under local stochastic volatility with jumps models in finance," European Journal of Operational Research, Elsevier, vol. 258(1), pages 358-371.
    8. Kenichiro Shiraya & Akihiko Takahashi, 2015. "Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models," CARF F-Series CARF-F-365, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. Lorenz Schneider & Bertrand Tavin, 2015. "Seasonal Stochastic Volatility and Correlation together with the Samuelson Effect in Commodity Futures Markets," Papers 1506.05911, arXiv.org.
    10. Kenichiro Shiraya & Akihiko Takahashi, 2017. "Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models (Revised version of CARF-F-365 : Forthcoming in Mathematics of Operations Research)," CARF F-Series CARF-F-426, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    11. Lorenz Schneider & Bertrand Tavin, 2018. "The Samuelson Effect and Seasonal Stochastic Volatility in Agricultural Futures Markets," Papers 1802.01393, arXiv.org.

    More about this item

    Keywords

    Spread option; Exchange option; Stochastic process; Characteristic function; Fourier inversion; Control variate;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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