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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

Puneet Pasricha Open the ORCID record for Puneet Pasricha [Opens in a new window]  and
Anubha Goel Open the ORCID record for Anubha Goel [Opens in a new window]
Puneet Pasricha
Affiliation:
Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India E-mails: pasrichapuneet5@gmail.com; anubha.goel1@gmail.com
Anubha Goel
Affiliation:
Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India E-mails: pasrichapuneet5@gmail.com; anubha.goel1@gmail.com
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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

double stochastic volatilityexchange optionsFeynman–Kac theoremHeston's stochastic volatility
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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