We build a sequence of empirical measures on the space $\mathbb{D}(\mathbb{R}_{+},\mathbb{R}^{d})$ 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.
@article{1233669886,
author = {Pag\`es, Gilles and Panloup, Fabien},
title = {Approximation of the distribution of a stationary Markov process with application to option pricing},
journal = {Bernoulli},
volume = {15},
number = {1},
year = {2009},
pages = { 146-177},
language = {en},
url = {http://dml.mathdoc.fr/item/1233669886}
}
Pagès, Gilles; Panloup, Fabien. Approximation of the distribution of a stationary Markov process with application to option pricing. Bernoulli, Tome 15 (2009) no. 1, pp. 146-177. http://gdmltest.u-ga.fr/item/1233669886/