Volatility models

The aim of this work is comparing two different models for estimating and forecasting the volatility of financial assets returns, the GARCH and the Stochastic Volatility (SV) model, applying their results to a daily Value at Risk model (VAR). The analysis consists, for each model, in a theoretical discussion and an empirical analysis carried out on a dataset containing S&P500 daily prices. The first part of the research is dedicated to the theoretical comparison and practical estimation of the two volatility models: for the SV model we introduce Bayesian analysis, MCMC methods such as the Gibbs Sampler and Metropolis Hastings algorithm. In the second part of the work we employ the two models variance predictions to build a daily VAR, identifying strengths and weaknesses of each volatility model from a VAR application point of view.