Information-based stochastic volatility model using the extended Kalman filter

Abstract

This study explores the use of non-linear filtering in an information-based stochastic volatility model. The stochastic differential equations in the model incorporate information which is the sum of true information about the future cash flows and noise which distorts the true information. It is assumed that there exists a market information process consisting of a combination of these two sources of information. The volatility process in the model is non-linear and gaussian which makes the use of the extended Kalman filter approach ideal. The study first obtains a state space model and the extended Kalman filter is then used to model volatility based on it. The modelled volatility is used to determine the extent to which the price of the information-based stochastic volatility model is affected by fluctuations in volatility. Using simulated data, the study finds that there’s a general increase in volatility as the price obtained from the model increases.