VOLATILITY MODELS AND THEIR APPLICATION TO OPTIONS PRICING AND RISK MANAGEMENT.

We look at various volatility models and their applications. Starting from a basic linear GARCH model we proceed to more advanced linear GARCH models involving leverage effects\ud and asymmetry. We also look at some examples of non-linear GARCH models such as TGARCH, smooth transition GARCH and NNGARCH. ML estimation technique is considered. Some applications to options pricing and risk management are presented. Next we turn our attention to discrete and continuous stochastic volatility models. Filtering techniques such as Kalman filter, particle filter are presented and estimation approaches based on filtering as well as efficient method of moments are elaborated on in details. Finally we take a look at the implied volatility surface and some ways of its estimation