## Bernoulli

• Bernoulli
• Volume 15, Number 1 (2009), 146-177.

### 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 $\mathbb{D}(\mathbb{R}_{+},\mathbb{R}^{d})$ of $ℝ^d$-valued cadlag 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 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.

#### Article information

Source
Bernoulli, Volume 15, Number 1 (2009), 146-177.

Dates
First available in Project Euclid: 3 February 2009

https://projecteuclid.org/euclid.bj/1233669886

Digital Object Identifier
doi:10.3150/08-BEJ142

Mathematical Reviews number (MathSciNet)
MR2546802

Zentralblatt MATH identifier
1214.60036

#### Citation

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

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