Abstract
We consider the estimation problem of stochastic volatility from stock data. The estimation of the volatility process of the Hull-White model is not in the usual frame work of the filtering theory. Discretizing the continuous Hull-White model to the discrete-time one, we can derive the exact volatility filter and realize this filter with the aid of particle filter algorithm. In this paper, we derive the optimal importance function and construct the particle filter algorithm for the discrete-time Hull-White model with jump processes. The parameters contained in system model are also estimated by constructing the augmented state for the volatility and parameters.
