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

Gilles Pag\`es and Fabien Panloup
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Gilles Pag\`es: PMA, LSProba
Fabien Panloup: PMA

Abstract: We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c\`adl\`ag 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 L\'evy 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.

Date: 2007-04, Revised 2009-09
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Published in Bernoulli 15, 1 (2009) 146-177

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:0704.0335

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