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Pricing Derivatives On Two-Dimensional Lévy Processes

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  • JOSÉ FAJARDO

    ()
    (IBMEC Business School, Av. Rio Branco 108. CEP 20040 001. Rio de Janeiro, Brazil)

  • ERNESTO MORDECKI

    ()
    (Facultad de Ciencias, Centro de Matemática, Iguá 4225, CP 11400, Montevideo, Uruguay)

Abstract

The aim of this work is to use a duality approach to study the pricing of derivatives depending on two stocks driven by a bidimensional Lévy process. The main idea is to apply Girsanov's Theorem for Lévy processes, in order to reduce the posed problem to a problem with one Lévy driven stock in an auxiliary market, baptized as "dual market". In this way, we extend the results obtained by Gerber and Shiu [5] for two-dimensional Brownian motion.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 09 (2006)
Issue (Month): 02 ()
Pages: 185-197

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Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:02:p:185-197

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Related research

Keywords: Lévy processes; optimal stopping; dual market method; derivative pricing;

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Cited by:
  1. Ernst Eberlein & Antonis Papapantoleon & Albert N. Shiryaev, 2008. "Esscher transform and the duality principle for multidimensional semimartingales," Science & Finance (CFM) working paper archive 0809.0301, Science & Finance, Capital Fund Management, revised Nov 2009.
  2. Ilya Molchanov & Michael Schmutz, 2009. "Exchangeability type properties of asset prices," Science & Finance (CFM) working paper archive 0901.4914, Science & Finance, Capital Fund Management, revised Apr 2011.
  3. José Fajardo & Ernesto Mordecki, 2008. "Symmetry and Time Changed Brownian Motions," IBMEC RJ Economics Discussion Papers 2008-02, Economics Research Group, IBMEC Business School - Rio de Janeiro.
  4. 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.

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