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.

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

JEL Classification: C3, C5, C6