- Volume 15, Number 1 (2009), 146-177.
Approximation of the distribution of a stationary Markov process with application to option pricing
We build a sequence of empirical measures on the space of ℝd-valued cadlag functions on ℝ+ in order to approximate the law of a stationary ℝd-valued Markov and Feller process (Xt). We obtain some general results on the convergence of this sequence. We then 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 provides an efficient means of option pricing in stochastic volatility models.
Bernoulli, Volume 15, Number 1 (2009), 146-177.
First available in Project Euclid: 3 February 2009
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Pagès, Gilles; Panloup, Fabien. Approximation of the distribution of a stationary Markov process with application to option pricing. Bernoulli 15 (2009), no. 1, 146--177. doi:10.3150/08-BEJ142. https://projecteuclid.org/euclid.bj/1233669886