Online Particle Filtering of Stochastic Volatility

A method for online estimation of the volatility when observing a stock price is proposed. This is based on modeling the volatility dynamics as a stochastic differential equation that is constructed using a technique from the control theory [1]. Identification of the model parameters using the observations is proposed afterwards [2]. It is based on some stochastic calculus. Volatility estimation is then reformulated as a filtering problem. An alternative filter instead of the optimal one is proposed since the latter is not computationally feasible. It is based on samples (or particles) drawn by discretization of the stochastic volatility model. Besides, the main feature that makes online particle filtering possible is analytic resolution of the Fokker-Planck equation for the current return. To the best of our knowledge, such technique for modeling together with online filtering of the volatility are quiet novel. The method is implemented on real data: the Heng Seng index price; this shows a period of relatively high volatility that corresponds obviously to the Asiatic crisis of October 1997.