Approximation of the Zakai equation for Diffusions with Noise Correlation and Its Application to Stochastic Volatility Estimation

Abstract

We study the splitting-up method for solving the Zakai equation for the diffusions with noise correlation. Using this approach, the numerical integration is decomposed into a stochastic step and deterministic one. In the stochastic step, we need to solve a first order hyperbolic equation. By using the method of a stochastic characteristic curve, the explicit form of the solution can be easily obtained. This approach is applied to solve the stochastic volatility estimation problem which arises in the mathematical finance filed.