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Pricing and hedging Margrabe options with stochastic volatilities

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Abstract

A Margrabe or exchange option is an option to exchange one asset for another. In a general stochastic volatility framework, by taking the second asset as a numeraire,we derive pricing as well as approximate pricing formulae for Margrabe options. The correlated Stein & Stein and the 3=2 model are studied as particular examples. Moreover, we derive the general mean-variance optimal hedging strategy and show that it is a delta-hedge only in case of zero correlation between asset prices and volatility.

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  • Elisa Alòs & Thorsten Rheinländer, 2015. "Pricing and hedging Margrabe options with stochastic volatilities," Economics Working Papers 1475, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 2017.
    • Handle: RePEc:upf:upfgen:1475
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    References listed on IDEAS

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    1. Fabio Antonelli & Sergio Scarlatti, 2009. "Pricing options under stochastic volatility: a power series approach," Finance and Stochastics, Springer, vol. 13(2), pages 269-303, April.
    2. Alos, Elisa & Ewald, Christian-Oliver, 2007. "Malliavin differentiability of the Heston volatility and applications to option pricing," MPRA Paper 3237, University Library of Munich, Germany.
    3. F. Antonelli & A. Ramponi & S. Scarlatti, 2010. "Exchange option pricing under stochastic volatility: a correlation expansion," Review of Derivatives Research, Springer, vol. 13(1), pages 45-73, April.
    4. Ewald, Christian-Oliver, 2008. "A note on the Malliavin derivative operator under change of variable," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 173-178, February.
    5. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
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    1. Gerald H. L. Cheang & Len Patrick Dominic M. Garces, 2020. "Representation of Exchange Option Prices under Stochastic Volatility Jump-Diffusion Dynamics," Papers 2002.10202, arXiv.org.
    2. Enrique Villamor & Pablo Olivares, 2023. "Valuing Exchange Options under an Ornstein-Uhlenbeck Covariance Model," IJFS, MDPI, vol. 11(2), pages 1-24, March.

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