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arXiv · 0704.0335

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

Gilles Pagès·Fabien Panloup
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Abstract

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.

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Gilles Pagès, Fabien Panloup. 2009-09-07. Approximation of the distribution of a stationary Markov process with application to option pricing. https://arxiv.org/abs/0704.0335

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