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Grupo de Estudos Monetários e Financeiros

Estudos do GEMF, N.º 10 de 2014


Stochastic Volatility Estimation with GPU Computing

António Alberto Santos

Faculdade de Economia, Universidade de Coimbra e GEMF

João Andrade
Instituto de Telecomunicações, Departamento de Engenharia Electrotécnica, Universidade de Coimbra

In this paper, we show how to estimate the parameters of stochastic volatility models using Bayesian estimation and Markov chain Monte Carlo (MCMC) simulations through the approximation of the a-posteriori distribution of parameters. Simulated independent draws are made possible by using Graphics Processing Units (GPUs) to compute several Markov chains in parallel. We show that the higher computational power of GPUs can be harnessed and put to good use by addressing two challenges. Bayesian estimation using MCMC simulations benefit from powerful processors since it is a complex numerical problem. Moreover, sequential approaches are characterized for drawing highly correlated samples which reduces the Effective Sample Size (ESS) associated with the simulated values obtained from the posterior distribution under a Bayesian analysis. However, under the proposed parallel expression of the algorithm, we show that a faster convergence rate is possible by running independent Markov chains, drawing lower correlations and therefore increase the ESS. The results obtained with this approach are presented for the Stochastic Volatility (SV) model, basic and with leverage.

JEL Classification: C11, C13, C15, C53, C63, C87.

Bayesian Estimation; Graphics Processing Unit; Parallel Computing; Simulation; State-Space Models; Stochastic Volatility.

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