On parameter estimation of Heston’s stochastic volatility model: a polynomial filtering method

Abstract

In this paper, we investigate the problem of estimating the volatility from the underlying asset price for discrete-time observations. This topic has attracted much research interest due to the key role of the volatility in finance. In this paper, we consider the Heston stochastic volatility model with jumps and we develop a new polynomial filtering method for the estimation of the volatility. The method relies on a linear filter which uses a polynomial state-space formulation of the discrete version of the continuous-time model. We demonstrate that a higher-order polynomial filtering method can be efficiently applied in the context of stochastic volatility models. Then, we compare our approach with some, well-established, techniques in the literature.