Markovian Projection Onto a Displaced Diffusion: Generic Formulas with Applications

International Journal of Theoretical and Applied Finance, Vol. 12, No. 4, pp. 507-522, 2009

Posted: 2 Dec 2009

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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.

Keywords: Markovian projection, displaced diffusion, LIBOR market model, cross-currency model, swaption, volatility skew

Suggested Citation

Antonov, Alexandre and Misirpashaev, Timur, Markovian Projection Onto a Displaced Diffusion: Generic Formulas with Applications. International Journal of Theoretical and Applied Finance, Vol. 12, No. 4, pp. 507-522, 2009, Available at SSRN: https://ssrn.com/abstract=1515527

Alexandre Antonov (Contact Author)

Danske Bank - Danske Markets ( email )

Holmens Kanal 2-12
DK-1092 Copenhagen K
Denmark

Timur Misirpashaev

Bloomberg LP ( email )

731 Lexington Ave
New York, NY 10022
United States

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