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The Malliavin Derivative and Application to Pricing and Hedging a European Exchange Option
Division of Actuarial Science, School of Management Studies, University of Cape Town, Cape Town, South Afric
- 1 Division of Actuarial Science, School of Management Studies, University of Cape Town, Cape Town, South Afric
Journal of Mathematical Finance·Volume 02 (2012)·Pages 280–290·Published 19 November 2012·DOI10.4236/jmf.2012.24031
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Abstract
The exchange option was introduced by Margrabe in [1] and its price was explicitly computed therein, albeit with some small variations to the models considered here. After that important introduction of an option to exchange one commodity for another, a lot more work has been devoted to variations of exchange options with attention focusing mainly on pricing but not hedging. In this paper, we demonstrate the efficiency of the Malliavin derivative in computing both the price and hedging portfolio of an exchange option. For that to happen, we first give a preview of white noise analysis and theory of distributions.
KeywordsExchange OptionContingent ClaimHedgingGeneralized CHO Formula
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