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Pricing Exchange Options under Stochastic Correlation

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  • Enrique Villamor

    (FIU)

  • Pablo Olivares

    (Ryerson University)

Abstract

In this paper we study the pricing of exchange options when underlying assets have stochastic volatility and stochastic correlation. An approximation using a closed-form approximation based on a Taylor expansion of the conditional price is proposed. Numerical results are illustrated for exchanges between WTI and Brent type oil prices.

Suggested Citation

  • Enrique Villamor & Pablo Olivares, 2020. "Pricing Exchange Options under Stochastic Correlation," Papers 2001.03967, arXiv.org.
    • Handle: RePEc:arx:papers:2001.03967
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    References listed on IDEAS

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    1. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
    2. Gerald Cheang & Carl Chiarella, 2011. "Exchange Options Under Jump-Diffusion Dynamics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(3), pages 245-276.
    3. Ruggero Caldana & Gerald H. L. Cheang & Carl Chiarella & Gianluca Fusai, 2015. "Correction: Exchange Option under Jump-diffusion Dynamics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(1), pages 99-103, March.
    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.
    5. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
    6. 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.
    7. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    8. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    9. Alexander Alvarez & Marcos Escobar & Pablo Olivares, 2011. "Pricing two dimensional derivatives under stochastic correlation," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 2(4), pages 265-287.
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