IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0809.0301.html
   My bibliography  Save this paper

Esscher transform and the duality principle for multidimensional semimartingales

Author

Listed:
  • Ernst Eberlein
  • Antonis Papapantoleon
  • Albert N. Shiryaev

Abstract

The duality principle in option pricing aims at simplifying valuation problems that depend on several variables by associating them to the corresponding dual option pricing problem. Here, we analyze the duality principle for options that depend on several assets. The asset price processes are driven by general semimartingales, and the dual measures are constructed via an Esscher transformation. As an application, we can relate swap and quanto options to standard call and put options. Explicit calculations for jump models are also provided.

Suggested Citation

  • Ernst Eberlein & Antonis Papapantoleon & Albert N. Shiryaev, 2008. "Esscher transform and the duality principle for multidimensional semimartingales," Papers 0809.0301, arXiv.org, revised Nov 2009.
  • Handle: RePEc:arx:papers:0809.0301
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0809.0301
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hans U. Gerber & Hlias S. W. Shiu, 1996. "Martingale Approach To Pricing Perpetual American Options On Two Stocks," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 303-322, July.
    2. Ernst Eberlein & Antonis Papapantoleon & Albert Shiryaev, 2008. "On the duality principle in option pricing: semimartingale setting," Finance and Stochastics, Springer, vol. 12(2), pages 265-292, April.
    3. José Fajardo & Ernesto Mordecki, 2006. "Pricing Derivatives On Two-Dimensional Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 185-197.
    Full references (including those not matched with items on IDEAS)

    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. Ilya Molchanov & Michael Schmutz, 2009. "Exchangeability type properties of asset prices," Papers 0901.4914, arXiv.org, revised Apr 2011.
    2. Christensen, Sören & Crocce, Fabián & Mordecki, Ernesto & Salminen, Paavo, 2019. "On optimal stopping of multidimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2561-2581.
    3. Pascal Louvet & Ollivier Taramasco, 2004. "Gouvernement d’entreprise:un modèle de répartition de la valeur créée entre dirigeant et actionnaire," Revue Finance Contrôle Stratégie, revues.org, vol. 7(1), pages 81-116, March.
    4. Dammann, Felix & Ferrari, Giorgio, 2021. "On an Irreversible Investment Problem with Two-Factor Uncertainty," Center for Mathematical Economics Working Papers 646, Center for Mathematical Economics, Bielefeld University.
    5. Decamps, Jean-Paul & Faure-Grimaud, Antoine, 2002. "Excessive continuation and dynamic agency costs of debt," European Economic Review, Elsevier, vol. 46(9), pages 1623-1644, October.
    6. Guanghua Lian & Robert J. Elliott & Petko Kalev & Zhaojun Yang, 2022. "Approximate pricing of American exchange options with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(6), pages 983-1001, June.
    7. Hainaut, Donatien, 2015. "Evaluation and default time for companies with uncertain cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 276-285.
    8. Junmin Shi & Michael Katehakis & Benjamin Melamed, 2013. "Martingale methods for pricing inventory penalties under continuous replenishment and compound renewal demands," Annals of Operations Research, Springer, vol. 208(1), pages 593-612, September.
    9. Nunes, Cláudia & Oliveira, Carlos & Pimentel, Rita, 2021. "Quasi-analytical solution of an investment problem with decreasing investment cost due to technological innovations," Journal of Economic Dynamics and Control, Elsevier, vol. 130(C).
    10. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "American options: the EPV pricing model," Annals of Finance, Springer, vol. 1(3), pages 267-292, August.
    11. Corsaro, Stefania & Kyriakou, Ioannis & Marazzina, Daniele & Marino, Zelda, 2019. "A general framework for pricing Asian options under stochastic volatility on parallel architectures," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1082-1095.
    12. Louberge, Henri & Villeneuve, Stephane & Chesney, Marc, 2002. "Long-term risk management of nuclear waste: a real options approach," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 157-180, November.
    13. Len Patrick Dominic M. Garces & Gerald H. L. Cheang, 2021. "A numerical approach to pricing exchange options under stochastic volatility and jump-diffusion dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 21(12), pages 2025-2054, December.
    14. 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.
    15. Hideharu Funahashi & Masaaki Kijima, 2017. "A unified approach for the pricing of options relating to averages," Review of Derivatives Research, Springer, vol. 20(3), pages 203-229, October.
    16. Fred Espen Benth & Hanna Zdanowicz, 2014. "Pricing and hedging of energy spread options and volatility modulated Volterra processes," Papers 1409.5801, arXiv.org.
    17. Christensen, Sören & Irle, Albrecht, 2020. "The monotone case approach for the solution of certain multidimensional optimal stopping problems," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1972-1993.
    18. Boyle, Phelim P. & Lin, X. Sheldon, 1997. "Bounds on contingent claims based on several assets," Journal of Financial Economics, Elsevier, vol. 46(3), pages 383-400, December.
    19. José Fajardo, 2014. "Symmetry and Bates’ rule in Ornstein–Uhlenbeck stochastic volatility models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 319-327, October.
    20. Rheinländer, Thorsten & Schmutz, Michael, 2013. "Self-dual continuous processes," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1765-1779.

    More about this item

    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:arx:papers:0809.0301. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.