IDEAS home Printed from https://ideas.repec.org/a/gam/jijfss/v11y2023i2p55-d1108730.html
   My bibliography  Save this article

Valuing Exchange Options under an Ornstein-Uhlenbeck Covariance Model

Author

Listed:
  • Enrique Villamor

    (Department of Mathematics, Florida International University, Miami, FL 33199, USA)

  • Pablo Olivares

    (Department of Mathematics, Toronto Metropolitan University, Toronto, ON M5B 2K3, Canada)

Abstract

In this paper we study the pricing of exchange options between two underlying assets whose dynamic show a stochastic correlation with random jumps. In particular, we consider a Ornstein-Uhlenbeck covariance model, with Levy Background Noise Processes driven by Inverse Gaussian subordinators. We use expansions in terms of Taylor polynomials and cubic splines to approximately compute the price of the derivative contract. Our findings show that the later approach provides an efficient way to compute the price when compared with a Monte Carlo method, while maintaining an equivalent degree of accuracy.

Suggested Citation

  • Enrique Villamor & Pablo Olivares, 2023. "Valuing Exchange Options under an Ornstein-Uhlenbeck Covariance Model," IJFS, MDPI, vol. 11(2), pages 1-24, March.
    • Handle: RePEc:gam:jijfss:v:11:y:2023:i:2:p:55-:d:1108730
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7072/11/2/55/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7072/11/2/55/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    4. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
    5. 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.
    6. Elisa Alòs & Thorsten Rheinländer, 2015. "Pricing and hedging Margrabe options with stochastic volatilities," Economics Working Papers 1475, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 2017.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Villamor, Enrique & Olivares, Pablo, 2024. "Pricing exchange options under stochastic correlation," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Enrique Villamor & Pablo Olivares, 2020. "Pricing Exchange Options under Stochastic Correlation," Papers 2001.03967, arXiv.org.
    2. Olivares Pablo & Villamor Enrique, 2017. "Valuing Exchange Options Under an Ornstein-Uhlenbeck Covariance Model," Papers 1711.10013, arXiv.org.
    3. Villamor, Enrique & Olivares, Pablo, 2024. "Pricing exchange options under stochastic correlation," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).
    4. Fred Espen Benth & Giulia Di Nunno & Asma Khedher & Maren Diane Schmeck, 2015. "Pricing of Spread Options on a Bivariate Jump Market and Stability to Model Risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(1), pages 28-62, March.
    5. Geonwoo Kim, 2020. "Valuation of Exchange Option with Credit Risk in a Hybrid Model," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    6. Ascione, Giacomo & Mehrdoust, Farshid & Orlando, Giuseppe & Samimi, Oldouz, 2023. "Foreign Exchange Options on Heston-CIR Model Under Lévy Process Framework," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    7. Matteo Gardini & Piergiacomo Sabino & Emanuela Sasso, 2020. "Correlating L\'evy processes with Self-Decomposability: Applications to Energy Markets," Papers 2004.04048, arXiv.org, revised Jul 2020.
    8. Richter, Anja, 2014. "Explicit solutions to quadratic BSDEs and applications to utility maximization in multivariate affine stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3578-3611.
    9. Fred Espen Benth & Hanna Zdanowicz, 2016. "Pricing And Hedging Of Energy Spread Options And Volatility Modulated Volterra Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-22, February.
    10. Fred Espen Benth & Hanna Zdanowicz, 2014. "Pricing and hedging of energy spread options and volatility modulated Volterra processes," Papers 1409.5801, arXiv.org.
    11. Branger, Nicole & Muck, Matthias, 2012. "Keep on smiling? The pricing of Quanto options when all covariances are stochastic," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1577-1591.
    12. Hangsuck Lee & Seongjoo Song & Gaeun Lee, 2023. "Insurance guaranty premiums and exchange options," Mathematics and Financial Economics, Springer, volume 17, number 3, December.
    13. Massoud Heidari & Liuren WU, 2002. "Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates?," Finance 0207013, University Library of Munich, Germany.
    14. José Fajardo & Ernesto Mordecki, 2005. "Duality and Derivative Pricing with Time-Changed Lévy Processes," IBMEC RJ Economics Discussion Papers 2005-12, Economics Research Group, IBMEC Business School - Rio de Janeiro.
    15. Fred Espen Benth & Jūratė Šaltytė Benth & Steen Koekebakker, 2008. "Stochastic Modeling of Electricity and Related Markets," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6811, December.
    16. Gerald H. L. Cheang & Len Patrick Dominic M. Garces, 2020. "Representation of Exchange Option Prices under Stochastic Volatility Jump-Diffusion Dynamics," Papers 2002.10202, arXiv.org.
    17. John Crosby, 2008. "Pricing a class of exotic commodity options in a multi-factor jump-diffusion model," Quantitative Finance, Taylor & Francis Journals, vol. 8(5), pages 471-483.
    18. 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).
    19. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    20. Fry-McKibbin, Renée & Martin, Vance L. & Tang, Chrismin, 2014. "Financial contagion and asset pricing," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 296-308.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jijfss:v:11:y:2023:i:2:p:55-:d:1108730. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.