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Markovian Projection Onto A Displaced Diffusion: Generic Formulas With Applications

Author

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  • A. ANTONOV

    (NumeriX Software Ltd., 41 Eastcheap Street, 2nd Floor, London EC3M 1DT, UK)

  • T. MISIRPASHAEV

    (NumeriX LLC, 4320 Winfield Road, Suite 200, Warrenville, IL 60555, USA)

Abstract

We develop a systematic approach to Markovian projection onto an effective displaced diffusion, and work out a set of computationally efficient formulas valid for a large class of non-Markovian underlying processes. The generic derivation is followed by applications, including the calculation of FX options in cross-currency models and swaption pricing in LIBOR Market Models, where we are able to recover in an unambiguous way many known analytical approximations and derive several new ones.

Suggested Citation

  • A. Antonov & T. Misirpashaev, 2009. "Markovian Projection Onto A Displaced Diffusion: Generic Formulas With Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 507-522.
    • Handle: RePEc:wsi:ijtafx:v:12:y:2009:i:04:n:s0219024909005300
    DOI: 10.1142/S0219024909005300
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    References listed on IDEAS

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    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(1), pages 1-32.
    3. Vladimir Piterbarg, 2005. "Stochastic Volatility Model with Time-dependent Skew," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(2), pages 147-185.
    4. Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
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