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Exchange Options Under Jump-Diffusion Dynamics

Author

Listed:
  • Gerald Cheang
  • Carl Chiarella

Abstract

This article extends the exchange option model of Margrabe, where the distributions of both stock prices are log-normal with correlated Wiener components, to allow the underlying assets to be driven by jump-diffusion processes of the type originally introduced by Merton. We introduce the Radon-Nikodym derivative process that induces the change of measure from the market measure to an equivalent martingale measure. The choice of parameters in the Radon-Nikodym derivative allows us to price the option under different financial-economic scenarios. We also consider American style exchange options and provide a probabilistic interpretation of the early exercise premium.

Suggested Citation

  • Gerald Cheang & Carl Chiarella, 2011. "Exchange Options Under Jump-Diffusion Dynamics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(3), pages 245-276.
    • Handle: RePEc:taf:apmtfi:v:18:y:2011:i:3:p:245-276
    DOI: 10.1080/1350486X.2010.505390
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    Cited by:

    1. He, Xin-Jiang & Wei, Wenting & Lin, Sha, 2025. "A closed-form formula for pricing exchange options with regime switching stochastic volatility and stochastic liquidity," International Review of Financial Analysis, Elsevier, vol. 103(C).
    2. 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).
    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. Hu, Dongdong & Sayit, Hasanjan & Yao, Jing & Zhong, Qifeng, 2024. "Closed-form approximations for basket option pricing under normal tempered stable Lévy model," The North American Journal of Economics and Finance, Elsevier, vol. 74(C).
    5. Pablo Olivares & Matthew Cane, 2014. "Pricing Spread Options under Stochastic Correlation and Jump-Diffusion Models," Papers 1409.1175, arXiv.org.
    6. Roman N. Makarov, 2023. "Option Pricing and Portfolio Optimization under a Multi-Asset Jump-Diffusion Model with Systemic Risk," Risks, MDPI, vol. 11(12), pages 1-24, December.
    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. Hangsuck Lee & Seongjoo Song & Gaeun Lee, 2023. "Insurance guaranty premiums and exchange options," Mathematics and Financial Economics, Springer, volume 17, number 3, March.
    9. Dongdong Hu & Hasanjan Sayit & Svetlozar T. Rachev, 2021. "Moment Matching Method for Pricing Spread Options with Mean-Variance Mixture L\'evy Motions," Papers 2109.02872, arXiv.org, revised Feb 2024.
    10. 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.
    11. Enrique Villamor & Pablo Olivares, 2020. "Pricing Exchange Options under Stochastic Correlation," Papers 2001.03967, arXiv.org.
    12. Enrique Villamor & Pablo Olivares, 2023. "Valuing Exchange Options under an Ornstein-Uhlenbeck Covariance Model," IJFS, MDPI, vol. 11(2), pages 1-24, March.
    13. Domenico De Giovanni & Arturo Leccadito & Debora Loccisano, 2024. "Co-movements, option pricing and risk management: an application to WTI versus Brent spread options," Annals of Operations Research, Springer, vol. 336(1), pages 1039-1061, May.
    14. 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.
    15. Olivares Pablo & Villamor Enrique, 2017. "Valuing Exchange Options Under an Ornstein-Uhlenbeck Covariance Model," Papers 1711.10013, arXiv.org.
    16. 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.
    17. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
    18. Zakaria Marah, 2023. "American Exchange option driven by a L\'evy process," Papers 2307.10900, arXiv.org.
    19. Kim, Geonwoo & Koo, Eunho, 2016. "Closed-form pricing formula for exchange option with credit risk," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 221-227.

    More about this item

    Keywords

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    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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