A novel multivariate stochastic volatility model and estimation with GPU computing

In this study, a novel multivariate stochastic volatility model is proposed for modeling the asset returns in financial markets. The proposed model can accommodate most of the common stylized facts such as the correlations between asset returns, leverage effect, cross-leverage effect and volatility spillovers and furthermore it allows replacing the static versions of the mentioned stylized facts with their time-varying (dynamic) counterparts completely or partially. Estimation algorithms based on the Markov Chain Monte Carlo (MCMC) methods in a Bayesian setting are also developed for the proposed model. Besides the MCMC based estimation algorithms, Sparse Grid Integration (SGI) based estimation algorithms which have not been previously applied to stochastic volatility estimation problems are also developed and evaluated in the study. Computational contributions of graphics processing units (GPUs) for estimation are assessed by developing parallel algorithms and implementing their programs on GPUs. Applications on simulated and empirical data show that the proposed model perform well in capturing the stylized facts and patterns of volatility in both static and dynamic settings. Numerical studies comparing the MCMC based estimation algorithms and the SGI based estimation algorithms show that the estimation algorithms based on the proposed approach (SGI) perform as well as the MCMC based algorithms and in certain conditions surpass the MCMC methods in terms of both accuracy and computational performance. In the simulation studies significant improvements in execution times are achieved with the implemented parallel algorithms on GPUs and the contribution of GPUs in practical applications of stochastic volatility estimation are illustrated.