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

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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https://hal.archives-ouvertes.fr/hal-00139496
Contributor : Fabien Panloup <>
Submitted on : Monday, September 7, 2009 - 2:55:27 PM
Last modification on : Thursday, December 10, 2020 - 10:56:20 AM
Long-term archiving on: : Friday, September 24, 2010 - 11:20:50 AM

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  • HAL Id : hal-00139496, version 4
  • ARXIV : 0704.0335

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Gilles Pagès, Fabien Panloup. Approximation of the distribution of a stationary Markov process with application to option pricing. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2009, 15 (1), pp.146-177. ⟨hal-00139496v4⟩

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