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Exchange Options when One Underlying Price Can Jump

Author

Listed:
  • François M. Quittard-Pinon
  • Rivo Randrianarivony

Abstract

Many problems in life insurance and finance can be described in terms of exchange options. These contracts give their holders the right to exchange an asset against another one at some specified later date. Exchange options were introduced in the classical diffusive framework where an explicit formula can be obtained for the price. This article extends this framework by taking jumps into account. In the particular case where one asset follows a jump diffusion model, the present authors present two alternative approaches for the pricing of these exchange options. The first one is a complete probabilistic approach where a quasi-closed form formula can be obtained. The second one is based on the generalized Fourier transform approach. With the latter, this article gives a general methodology for pricing exchange options when one underlying can jump. This methodology can then be used in many areas such as the study of guaranteed funds in life insurance.

Suggested Citation

  • François M. Quittard-Pinon & Rivo Randrianarivony, 2010. "Exchange Options when One Underlying Price Can Jump," Finance, Presses universitaires de Grenoble, vol. 31(1), pages 33-53.
    • Handle: RePEc:cai:finpug:fina_311_0033
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    References listed on IDEAS

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    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    7. 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.
    8. José Fajardo & Ernesto Mordecki, 2006. "Pricing Derivatives On Two-Dimensional Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 185-197.
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    Cited by:

    1. Len Patrick Dominic M. Garces & Gerald H. L. Cheang, 2021. "A Numerical Approach to Pricing Exchange Options under Stochastic Volatility and Jump-Diffusion Dynamics," Papers 2106.07362, arXiv.org.
    2. Len Patrick Dominic M. Garces & Gerald H. L. Cheang, 2020. "A Put-Call Transformation of the Exchange Option Problem under Stochastic Volatility and Jump Diffusion Dynamics," Papers 2002.10194, arXiv.org.
    3. Pasricha, Puneet & He, Xin-Jiang, 2022. "Skew-Brownian motion and pricing European exchange options," International Review of Financial Analysis, Elsevier, vol. 82(C).
    4. Len Patrick Dominic M. Garces & Gerald H. L. Cheang, 2021. "A numerical approach to pricing exchange options under stochastic volatility and jump-diffusion dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 21(12), pages 2025-2054, December.

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