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A CLOSED-FORM PRICING FORMULA FOR EUROPEAN EXCHANGE OPTIONS WITH STOCHASTIC VOLATILITY
Published online by Cambridge University Press: 05 January 2021
Abstract
This article derives a closed-form pricing formula for the European exchange option in a stochastic volatility framework. Firstly, with the Feynman–Kac theorem's application, we obtain a relation between the price of the European exchange option and a European vanilla call option with unit strike price under a doubly stochastic volatility model. Then, we obtain the closed-form solution for the vanilla option using the characteristic function. A key distinguishing feature of the proposed simplified approach is that it does not require a change of numeraire in contrast with the usual methods to price exchange options. Finally, through numerical experiments, the accuracy of the newly derived formula is verified by comparing with the results obtained using Monte Carlo simulations.
Keywords
- Type
- Research Article
- Information
- Probability in the Engineering and Informational Sciences , Volume 36 , Issue 3 , July 2022 , pp. 606 - 615
- Copyright
- Copyright © The Author(s), 2020. Published by Cambridge University Press
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