Markovian Projection Onto a Displaced Diffusion: Generic Formulas with Applications

18 Pages Posted: 17 Oct 2006

Multiple version iconThere are 2 versions of this paper

Date Written: October 9, 2006

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, Cross Currency Libor Market Models with Skew, FX volatility skew, LMM swaption formula

JEL Classification: C3, C5, C6

Suggested Citation

Antonov, Alexandre and Misirpashaev, Timur, Markovian Projection Onto a Displaced Diffusion: Generic Formulas with Applications (October 9, 2006). Available at SSRN: https://ssrn.com/abstract=937860 or http://dx.doi.org/10.2139/ssrn.937860

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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