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Duality and Derivative Pricing with Time-Changed Lévy Processes

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Economics Research Group, IBMEC Business School - Rio de Janeiro in its series IBMEC RJ Economics Discussion Papers with number 2005-12.

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Date of creation: 29 Nov 2005
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Handle: RePEc:ibr:dpaper:2005-12

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Related research

Keywords: Lévy processes; Time Change; Symmetry;

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References

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  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. 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 637-54, May-June.
  3. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
  4. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  5. 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.
  6. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-86, March.
  7. 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.
  8. 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.
  9. Schroder, Mark, 1999. "Changes of Numeraire for Pricing Futures, Forwards, and Options," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1143-63.
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Citations

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Cited by:
  1. José Fajardo & Ernesto Mordecki, 2009. "Skewness Premium with Lévy Processes," CREATES Research Papers 2009-10, School of Economics and Management, University of Aarhus.
  2. Ilya Molchanov & Michael Schmutz, 2009. "Exchangeability type properties of asset prices," Papers 0901.4914, arXiv.org, revised Apr 2011.

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