Approximation of the distribution of a stationary Markov process with application to option pricing

Abstract

We build a sequence of empirical measures on the space D(ℝ +, ℝd) of ℝd-valued cadlag functions on R+ in order to approximate the law of a stationary ℝd-valued Markov and Feller process (Xt). We obtain some general results on the convergence of this sequence. We then apply them to Brownian diffusions and solutions to Lévy-driven SDE's under some Lyapunov-type stability assumptions. As a numerical application of this work, we show that this procedure provides an efficient means of option pricing in stochastic volatility models. © 2009 ISI/BS.