Abstract

This paper presents and implements a novel stochastic volatility (SV) model, based on the structure of the GARCH model, to describe the relationship between an observed financial return series and its standard deviation, namely volatility. The proposed approach has been compared to the standard GARCH as the underlying modeling structure within a particle-filtering-based scheme for state estimation. The proposed structure has been implemented to estimate the volatility of both a simulated return series and the NASDAQ Composite index during the period July 21, 2008 - July 17, 2009. The results of this procedure show that the parameters of the GARCH model can be used in the uGARCH structure, allowing the latter representing the hidden volatility as accurate as the standard GARCH, but also providing an estimate of the whole probability density.