Markovian Projection onto a Displaced Diffusion: Generic Formulas with Applications

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.

Number of Pages in PDF File: 18

Keywords: Markovian projection, displaced diffusion, Cross Currency Libor Market Models with Skew, FX volatility skew, LMM swaption formula

JEL Classification: C3, C5, C6

working papers series