Stochastic Volatility Models: MCMC Estimation and Forecasting

Nicholas Sobieski Hansen & Tayyab Ahmad

Student thesis: Master thesis

Abstract

The purpose of this thesis is to gain a profound knowledge and understanding for Stochastic Volatility (SV ) Models and Markov Chain Monte Carlo (MCMC) methods in order to apply these methods to estimation and prediction with real world data. SV models are an alternative to the widely used ARCH and GARCH type models and differ in their assumption that the volatility itself follows a stochastic process. However, this reformulation of the volatility process makes the estimation more complicated since the likelihood function is untraceable. To overcome this, MCMC methods among others can be used for the estimation procedure. This paper utilizes MCMC methods to conduct inference by obtaining samples from the posterior distribution of parameters and latent variables from the SV models which can be used for predicting future volatilities. During the thesis, Metropolis Hastings and Gibbs sampling algorithms will be thoroughly described and supplemented with simulation studies having the intention of giving a better and broader understanding of the methods. For the practical applications in the analysis data from the S&P 500 index was chosen. The R package "Stochvol" was utilized for the estimation and prediction section as it showed excellent results in simulation studies. From the results in the analysis we choose only to exploit the SV model as it was a better fit than the SVt model. Hence, the SV model showed to work as intended in the out of sample forecasting as the prediction intervals continuously adapted as high and low volatility was captured. Finally, we can conclude that it is possible to estimate and predict in the SV model with MCMC methods.

EducationsMSc in Business Administration and Management Science, (Graduate Programme) Final Thesis
LanguageDanish
Publication date2020
Number of pages101
SupervisorsAnders Rønn-Nielsen