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

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

2007-04-03

arxiv.org/abs/0704.0335v3

Bernoulli 15, 1 (2009) 146-177

Mathematics

Probability

Scientific paper

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.

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