IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v18y2011i3p245-276.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.505390
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/1350486X.2010.505390?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mark Broadie & Jérôme Detemple, 1997. "The Valuation of American Options on Multiple Assets," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 241-286, July.
    2. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
    3. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. David B. Colwell & Robert J. Elliott, 1993. "Discontinuous Asset Prices And Non‐Attainable Contingent Claims1," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 295-308, July.
    5. Chandrasekhar Reddy Gukhal, 2001. "Analytical Valuation of American Options on Jump‐Diffusion Processes," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 97-115, January.
    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. 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).
    2. Hangsuck Lee & Seongjoo Song & Gaeun Lee, 2023. "Insurance guaranty premiums and exchange options," Mathematics and Financial Economics, Springer, volume 17, number 3, December.
    3. 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.
    4. Enrique Villamor & Pablo Olivares, 2020. "Pricing Exchange Options under Stochastic Correlation," Papers 2001.03967, arXiv.org.
    5. Enrique Villamor & Pablo Olivares, 2023. "Valuing Exchange Options under an Ornstein-Uhlenbeck Covariance Model," IJFS, MDPI, vol. 11(2), pages 1-24, March.
    6. Olivares Pablo & Villamor Enrique, 2017. "Valuing Exchange Options Under an Ornstein-Uhlenbeck Covariance Model," Papers 1711.10013, arXiv.org.
    7. 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.
    8. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
    9. Zakaria Marah, 2023. "American Exchange option driven by a L\'evy process," Papers 2307.10900, arXiv.org.
    10. Villamor, Enrique & Olivares, Pablo, 2024. "Pricing exchange options under stochastic correlation," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).
    11. Pablo Olivares & Matthew Cane, 2014. "Pricing Spread Options under Stochastic Correlation and Jump-Diffusion Models," Papers 1409.1175, arXiv.org.
    12. 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.
    13. 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.
    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. 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.

    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. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    2. B. Gao J. Huang, "undated". "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-002, New York University, Leonard N. Stern School of Business-.
    3. Jérôme Detemple, 1999. "American Options: Symmetry Properties," CIRANO Working Papers 99s-45, CIRANO.
    4. Li Chen & Guang Zhang, 2021. "Hermite Polynomial-based Valuation of American Options with General Jump-Diffusion Processes," Papers 2104.11870, arXiv.org.
    5. Carl Chiarella & Andrew Ziogas, 2009. "American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 37-79.
    6. S H Martzoukos, 2009. "Real R&D options and optimal activation of two-dimensional random controls," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(6), pages 843-858, June.
    7. Jérôme Detemple & Weidong Tian, 2002. "The Valuation of American Options for a Class of Diffusion Processes," Management Science, INFORMS, vol. 48(7), pages 917-937, July.
    8. Lian, Yu-Min & Chen, Jun-Home & Liao, Szu-Lang, 2021. "Cojump risks and their impacts on option pricing," The Quarterly Review of Economics and Finance, Elsevier, vol. 79(C), pages 399-410.
    9. Lian, Yu-Min & Chen, Jun-Home, 2020. "Joint dynamic modeling and option pricing in incomplete derivative-security market," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).
    10. Gao, Bin & Huang, Jing-zhi & Subrahmanyam, Marti, 2000. "The valuation of American barrier options using the decomposition technique," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1783-1827, October.
    11. Hao Zhou & Duy-Minh Dang, 2024. "Numerical analysis of American option pricing in a two-asset jump-diffusion model," Papers 2410.04745, arXiv.org, revised Oct 2024.
    12. Andrew Ziogas & Carl Chiarella, 2003. "McKean’s Method applied to American Call Options on Jump-Diffusion Processes," Computing in Economics and Finance 2003 39, Society for Computational Economics.
    13. Gerald H.L. Cheang & Carl Chiarella, 2008. "Hedge Portfolios in Markets with Price Discontinuities," Research Paper Series 218, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Alfredo Ibáñez, 2003. "Robust Pricing of the American Put Option: A Note on Richardson Extrapolation and the Early Exercise Premium," Management Science, INFORMS, vol. 49(9), pages 1210-1228, September.
    15. Carl Chiarella & Jonathan Ziveyi, 2014. "Pricing American options written on two underlying assets," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 409-426, March.
    16. Gerald H. L. Cheang & Carl Chiarella & Andrew Ziogas, 2013. "The representation of American options prices under stochastic volatility and jump-diffusion dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 13(2), pages 241-253, January.
    17. Detemple, Jérôme & Emmerling, Thomas, 2009. "American chooser options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 128-153, January.
    18. Vidal Nunes, João Pedro & Ruas, João Pedro & Dias, José Carlos, 2020. "Early exercise boundaries for American-style knock-out options," European Journal of Operational Research, Elsevier, vol. 285(2), pages 753-766.
    19. Arve, Malin & Zwart, Gijsbert, 2023. "Optimal procurement and investment in new technologies under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 147(C).
    20. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.

    More about this item

    Keywords

    American options; exchange options; compound Poisson processes; equivalent martingale measure;
    All these keywords.

    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

    Statistics

    Access and download statistics

    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:taf:apmtfi:v:18:y:2011:i:3:p:245-276. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    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.