MARKOVIAN PROJECTION ONTO A DISPLACED DIFFUSION: GENERIC FORMULAS WITH APPLICATIONS

A. Antonov () and T. Misirpashaev ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2009, vol. 12, issue 04, 507-522

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 (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1142/S0219024909005300

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