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.
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References
Bjerksund, P., Stensland, G.: Closed form spread option valuation. Quant. Finance 14(10), 1785–1794 (2014)
Carmona, R., Durrleman, V.: Pricing and hedging spread options. SIAM Rev. 45(4), 627–685 (2003)
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)
Clewlow, L., Strickland, C.: Energy Derivatives: Pricing and Risk Management. Lacima Publications, London (2000)
Geman, H.: Commodities and Commodity Derivatives: Modeling and Pricing for Agriculturals, Metals and Energy. Wiley, London (2005)
Li, M., Deng, S.-J., Zhou, J.: Closed-form approximations for spread option prices and Greeks. J. Deriv. 15(3), 58–80 (Spring 2008)
Margrabe, W.: The value of an option to exchange one asset for another. J. Finance 33(1), 177–186 (1978)
Pilipovic, D.: Energy Risk: Valuing and Managing Energy Derivatives, 2nd edn. McGraw-Hill, New York (2007)
Tong, Y.L.: The Multivariate Normal Distribution. Springer Series in Statistics. Springer, New York (1990)
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)
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.
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Tuenter, H.J.H. (2015). Margrabe Revisited. In: Aïd, R., Ludkovski, M., Sircar, R. (eds) Commodities, Energy and Environmental Finance. Fields Institute Communications, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2733-3_4
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