Bayesian techniques for discrete stochastic volatility models

Abstract

Reliable volatility forecasts are needed in many areas of nance, be it option pricing, risk management or portfolio allocation. Mathematical models that capture temporal dependencies between the returns of nancial assets and their volatility and could be used for volatility forecasting generally fall into one of the following categories: historical volatility models, GARCH { type models and Stochastic Volatility (SV) models. This thesis will focus on the predictive ability of the discrete version of SV models. Six variants of discrete SV models will be estimated: classic SV model, SV model with innovations having Student distribution, SV model with Gaussian innovations augmented with lag one trading volume, SV model with t-innovations augmented with lag one trading volume, SV model with Gaussian innovations augmented with lag two trading volume, SV model with t-innovations augmented with lag two trading volume. These models will be compared on the basis of their ability to predict volatility. Our study will show that SV model specification with Student t distribution with 3 degrees of freedom leads to a significant improvement in volatility forecasts, thus demonstrating good agreement with the empirical fact that financial returns have fat-tailed distribution. It will be shown that the influence of the trading volume is very small compared with the impact of different distributional assumptions on innovations.