Approximation of the distribution of a stationary Markov process with application to option pricing (Q605850)

The authors consider the Feller-Markov process which admits an invariant distribution and propose a way to approximate the stationary distribution of this process. More precisely, they construct a sequence of empirical measures on the Skorokhod space and obtain some general results on the convergence of this sequence. The results are applied to Brownian diffusions and solutions to Lévy-driven stochastic differential equations under some Lyapunov-type stability assumptions. As a numerical application, the authors construct a numerical method for option pricing in stationary stochastic volatility models where the volatility evolves under its stationary regime.