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Pricing exchange options under stochastic correlation

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  • Villamor, Enrique
  • Olivares, Pablo

Abstract

In this paper we study the pricing of exchange options when the underlying assets have stochastic volatility and stochastic correlation. An approximated closed-form formula based on a Taylor expansion of the conditional Margrabe price is proposed. The problem is illustrated within the framework of the exchange between two different types of oil commodities.

Suggested Citation

  • Villamor, Enrique & Olivares, Pablo, 2024. "Pricing exchange options under stochastic correlation," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).
    • Handle: RePEc:eee:ecofin:v:73:y:2024:i:c:s1062940824000780
    DOI: 10.1016/j.najef.2024.102153
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    References listed on IDEAS

    as
    1. Gerald Cheang & Carl Chiarella, 2011. "Exchange Options Under Jump-Diffusion Dynamics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(3), pages 245-276.
    2. Puneet Pasricha & Song-Ping Zhu & Xin-Jiang He, 2022. "A closed-form pricing formula for European options in an illiquid asset market," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-18, December.
    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. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    5. Fazlollah Soleymani & Andrey Itkin, 2019. "Pricing foreign exchange options under stochastic volatility and interest rates using an RBF--FD method," Papers 1903.00937, arXiv.org.
    6. Wang, Guanying & Wang, Xingchun & Shao, Xinjian, 2022. "Exchange options for catastrophe risk management," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    7. Geonwoo Kim, 2020. "Valuation of Exchange Option with Credit Risk in a Hybrid Model," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    8. Enrique Villamor & Pablo Olivares, 2023. "Valuing Exchange Options under an Ornstein-Uhlenbeck Covariance Model," IJFS, MDPI, vol. 11(2), pages 1-24, March.
    9. Stefanie Engel & Charles Palmer & Luca Taschini & Simon Urech, 2015. "Conservation Payments under Uncertainty," Land Economics, University of Wisconsin Press, vol. 91(1), pages 36-56.
    10. Pablo Olivares & Alexander Alvarez, 2016. "Pricing Basket Options by Polynomial Approximations," Journal of Applied Mathematics, Hindawi, vol. 2016, pages 1-12, October.
    11. Kim, Jeong-Hoon & Park, Chang-Rae, 2017. "A multiscale extension of the Margrabe formula under stochastic volatility," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 59-65.
    12. 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.
    13. 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.
    14. 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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    More about this item

    Keywords

    Exchange options; Stochastic correlation; Taylor expansion; Ornstein–Uhlenbeck process;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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