Abstract
We build a sequence of empirical measures on the space $\mathbb{D}(\mathbb{R}_{+},\mathbb{R}^{d})$ of $ℝ^d$-valued cadlag 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 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.
Citation
Gilles Pagès. Fabien Panloup. "Approximation of the distribution of a stationary Markov process with application to option pricing." Bernoulli 15 (1) 146 - 177, February 2009. https://doi.org/10.3150/08-BEJ142
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