Margrabe Revisited

Part of the Fields Institute Communications book series (FIC, volume 74)

Abstract

We introduce a new representation of the bivariate normal distribution to first give a short derivation of the classic Margrabe exchange-option formula, using elementary integration methods. The second application is a new and simple technique to provide an accurate lower bound for the value of a spread option with a nonzero strike.

Keywords

Volatility 

Notes

Acknowledgements

The simplified proof of the Margrabe formula, using elementary integration techniques, was developed in the context of a course on energy commodities that the author teaches in the Mathematical Finance Program at the University of Toronto. I thank the anonymous referee for comments and suggestions that helped to improve the presentation, and my wife Marguerite Martindale for a professional line edit.

References

  1. 1.
    Bjerksund, P., Stensland, G.: Closed form spread option valuation. Quant. Finance 14(10), 1785–1794 (2014)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Carmona, R., Durrleman, V.: Pricing and hedging spread options. SIAM Rev. 45(4), 627–685 (2003)MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Carmona, R., Durrleman, V.: Pricing and hedging spread options in a log-normal model. Technical Report, Department of Operations Research and Financial Engineering. Princeton University, Princeton, NJ, 16 March (2003)Google Scholar
  4. 4.
    Clewlow, L., Strickland, C.: Energy Derivatives: Pricing and Risk Management. Lacima Publications, London (2000)Google Scholar
  5. 5.
    Geman, H.: Commodities and Commodity Derivatives: Modeling and Pricing for Agriculturals, Metals and Energy. Wiley, London (2005)Google Scholar
  6. 6.
    Li, M., Deng, S.-J., Zhou, J.: Closed-form approximations for spread option prices and Greeks. J. Deriv. 15(3), 58–80 (Spring 2008)CrossRefGoogle Scholar
  7. 7.
    Margrabe, W.: The value of an option to exchange one asset for another. J. Finance 33(1), 177–186 (1978)CrossRefGoogle Scholar
  8. 8.
    Pilipovic, D.: Energy Risk: Valuing and Managing Energy Derivatives, 2nd edn. McGraw-Hill, New York (2007)Google Scholar
  9. 9.
    Tong, Y.L.: The Multivariate Normal Distribution. Springer Series in Statistics. Springer, New York (1990)MATHCrossRefGoogle Scholar
  10. 10.
    van der Hoek, J., Korolkiewicz, M.W.: New analytic approximations for pricing spread options. In: Cohen, S.N., Madan, D., Siu, T.K.,Yang, H. (eds.) Stochastic Processes, Finance and Control: A Festschrift in Honor of Robert J. Elliott. Advances in Statistics, Probability and Actuarial Science, vol. 1, pp. 259–284. World Scientific, Singapore (2012)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Mathematical Finance ProgramUniversity of TorontoTorontoCanada

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