A study of the heston stochastic volatility model

Abstract

The aim of this dissertation is to provide an introduction to stochastic differential equations followed by the study of stochastic volatility models. This will enable us to analyze the dynamics of the S&P500 index under the stochastic volatility assumption. In particular, the Heston stochastic volatility model will be developed. Also, some properties of the Heston stochastic volatility model will be looked into and the model will be implemented on the S&P500 index data. To estimate the parameters of the model, the Kalman and Extended Kalman filters will be studied. A discussion on the method used and the results extracted will follow in the end.