Stochastic Volatility Estimation with Application to Option Pricing

We consider the estimation problem of the stochastic volatility in the Hull-White framework. We consider the stock price as the observation and pose the estimation problem for the stochastic volatility. We first show that it is not possible to formulate this as a usual filtering problem and propose an alternative formulation. We then derive the robust filtering equation suitable for real observation data and apply this new filter to the option pricing problem.