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

## TL;DR

This paper develops a method to approximate the distribution of stationary Markov processes, with applications to option pricing in stochastic volatility models, through empirical measures and convergence analysis.

## Contribution

It introduces a new approach to approximate stationary Markov process distributions and applies it to option pricing, demonstrating efficiency in stochastic volatility models.

## Key findings

- Convergence results for empirical measures approximating Markov processes.
- Application to Brownian diffusions and Lévy-driven SDEs under stability conditions.
- Efficient numerical method for option pricing in complex models.

## Abstract

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.