Analytic approximation of the transition densityfunction under a multi-scale volatility model

Abstract

The transition density function plays an important role in understanding and explainingthe dynamics of the stochastic process. We propose an approach which can be used forthe analytic approximation of the transition density related to a multi-scale stochasticvolatility model. Using perturbation theory, we compute the leading-order term and thefirst-order correction terms. A numerical test also confirms the effectiveness of the model.