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Pré-Publication, Document De Travail Année : 2007

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

Gilles Pagès
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  • IdHAL : gilpag
Fabien Panloup
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  • PersonId : 839160

Résumé

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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Dates et versions

hal-00139496 , version 1 (31-03-2007)
hal-00139496 , version 2 (02-04-2007)
hal-00139496 , version 3 (23-02-2009)
hal-00139496 , version 4 (07-09-2009)

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Gilles Pagès, Fabien Panloup. Approximation of the distribution of a stationary Markov process with application to option pricing. 2007. ⟨hal-00139496v2⟩
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