Stochastic volatility with big data

Abstract

The thesis aims to discuss stochastic volatility when a big amount of data is involved. Therefore I follow Windle and Carvalho (2015) and Casarin (2015) papers where a state-space model for observations and latent variables in the space of positive symmetric matrices is introduced. Moreover, I use Gibbs sample and MCMC method in order to discuss the Bayesian inference. One-step ahead and multi-step-ahead forecasting are evaluated because of their importance in economics and business. Since this model can have important applications in finance, one can use realized covariance matrices as data to predict latent time-varying covariance matrices. I present factor-like models, GARCH-like model and univariate stochastic volatility models to give an alternative to the model from the mentioned papers.

It is known that financial markets data often expose volatility clustering, where time series have periods of high volatility and periods of low volatility. As a matter of fact, time-varying volatility appears more than constant volatility, and accurate modelling of time-varying volatility is of great importance, considering economic and financial data. In our case working with a nonlinear model by using MCMC posterior approximation can be a quite challenging issue. Computational time in Monte Carlo simulations is reduced by implementing a parallel algorithm in Matlab which is able to split our database and run the blocks in the same time.