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

Gilles Pagès (1, 2) , Fabien Panloup (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 LSP - Laboratoire de Statistique et Probabilités

We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued càdlàg functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t). We obtain some general results of convergence of this sequence. Then, we 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 gives an efficient way of option pricing in stochastic volatility models.

Mots clés: stationary process; numerical approximation; Lévy process; Euler scheme; option pricing; stochastic volatility model

Domaines: Probabilités [math.PR]

Gilles Pagès, Fabien Panloup. Approximation of the distribution of a stationary Markov process with application to option pricing. Bernoulli, 2009, 15 (1), pp.146-177. ⟨hal-00139496v4⟩