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Duality and Derivative Pricing with Time-Changed Lévy Processes

Author

Listed:
  • José Fajardo

    (IBMEC Business School - Rio de Janeiro)

  • Ernesto Mordecki

    (Centro de Matemática, Facultad de Ciências, Universidad de la República, Uruguay)

Abstract

In this paper we study the pricing problem of derivatives written in terms of a two dimensional Time-changed Lévy processes. Then, we examine an existing relation between prices of put and call options, of both the European and the American type. This relation is called put-call duality. It includes as a particular case, the relation known as put-call symmetry. Necessary and sufficient conditions for put-call symmetry to hold are shown, in terms of the triplet of local characteristic of the Time-changed Lévy process. In this way we extend the results obtained by Fajardo and Mordecki (2004a) and Fajardo and Mordecki (2004b) to the case of Time-changed Lévy processes.

Suggested Citation

  • 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.
    • Handle: RePEc:ibr:dpaper:2005-12
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    File URL: http://professores.ibmecrj.br/erg/dp/papers/dp200512.pdf
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    References listed on IDEAS

    as
    1. Fajardo, J. & Mordecki, E., 2003. "Put-Call Duality and Symmetry," Finance Lab Working Papers flwp_54, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    3. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," The Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
    4. Jing-zhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time-Changed Lévy Processes," Journal of Finance, American Finance Association, vol. 59(3), pages 1405-1440, June.
    5. Schroder, Mark, 1999. "Changes of Numeraire for Pricing Futures, Forwards, and Options," The Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1143-1163.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. 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.
    9. 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.
    10. 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.
    11. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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    Cited by:

    1. José Fajardo & Ernesto Mordecki, 2006. "Skewness Premium with Lévy Processes," IBMEC RJ Economics Discussion Papers 2006-04, Economics Research Group, IBMEC Business School - Rio de Janeiro.
    2. Fajardo, José & Mordecki, Ernesto, 2010. "Market symmetry in time-changed Brownian models," Finance Research Letters, Elsevier, vol. 7(1), pages 53-59, March.

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    More about this item

    Keywords

    Lévy processes; Time Change; Symmetry;
    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

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