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Asymptotic Analysis For Foreign Exchange Derivatives With Stochastic Volatility

Author

Listed:
  • CHARLES CUTHBERTSON

    (Department of Statistics, University of Oxford, OX1 3TG, UK)

  • GRIGORIOS PAVLIOTIS

    (Department of Mathematics, Imperial College London, SW7 2AZ, UK)

  • AVRAAM RAFAILIDIS

    (Department of Mathematics, King's College London, WC2R 2LS, UK)

  • PETTER WIBERG

    (Mathematics Institute, The University of Warwick, Coventry CV4 7AL, UK)

Abstract

We consider models for the valuation of derivative securities that depend on foreign exchange rates. We derive partial differential equations for option prices in an arbitrage-free market with stochastic volatility. By use of standard techniques, and under the assumption of fast mean reversion for the volatility, these equations can be solved asymptotically. The analysis goes further to consider specific examples for a number of options, and to a considerable degree of complexity.

Suggested Citation

  • Charles Cuthbertson & Grigorios Pavliotis & Avraam Rafailidis & Petter Wiberg, 2010. "Asymptotic Analysis For Foreign Exchange Derivatives With Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(07), pages 1131-1147.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:07:n:s0219024910006145
    DOI: 10.1142/S0219024910006145
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    References listed on IDEAS

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    1. Stephen J. Taylor, 2007. "Introduction to Asset Price Dynamics, Volatility, and Prediction," Introductory Chapters, in: Asset Price Dynamics, Volatility, and Prediction, Princeton University Press.
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