Stochastic Volatility Estimation with GPU Computing

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.

[1]  Yasuhiro Omori,et al.  Multivariate Stochastic Volatility Model with Cross Leverage , 2010, COMPSTAT.

[2]  Yasuhiro Omori,et al.  Leverage, heavy-tails and correlated jumps in stochastic volatility models , 2007, Comput. Stat. Data Anal..

[3]  T. Bollerslev.  Generalized autoregressive conditional heteroskedasticity with applications in finance , 1986 .

[4]  Sylvia Richardson,et al.  Markov chain concepts related to sampling algorithms , 1995 .

[5]  L. Agnello,et al.  How does fiscal policy react to wealth composition and asset prices , 2012 .

[6]  Peter E. Rossi,et al.  Bayesian Analysis of Stochastic Volatility Models , 1994 .

[7]  N. Shephard,et al.  Analysis of high dimensional multivariate stochastic volatility models , 2006 .

[8]  N. Shephard,et al.  Markov chain Monte Carlo methods for stochastic volatility models , 2002 .

[9]  N. Shephard.  Statistical aspects of ARCH and stochastic volatility , 1996 .

[10]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[11]  Stephen L Taylor,et al.  Modelling Financial Time Series , 1987 .

[12]  John D. Owens,et al.  GPU Computing , 2008, Proceedings of the IEEE.

[13]  Peter E. Rossi,et al.  Bayesian Analysis of Stochastic Volatility Models: Comments: Reply , 1994 .

[14]  Jun Yu.  On Leverage in a Stochastic Volatility Model , 2004 .

[15]  S. E. Ahmed,et al.  Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference , 2008, Technometrics.

[16]  Walter R. Gilks,et al.  Introduction to general state-space Markov chain theory , 1995 .

[17]  R. Beran.  The Impact of the Bootstrap on Statistical Algorithms and Theory , 2003 .

[18]  J. Andrade,et al.  Convergence and Growth: Portugal in the EU 1986-2010 , 2012 .

[19]  David J. Spiegelhalter,et al.  Introducing Markov chain Monte Carlo , 1995 .

[20]  David Blythe,et al.  Rise of the Graphics Processor , 2008, Proceedings of the IEEE.

[21]  Arnaud Doucet,et al.  On the Utility of Graphics Cards to Perform Massively Parallel Simulation of Advanced Monte Carlo Methods , 2009, Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America.

[22]  Tübinger Diskussionsbeiträge,et al.  Stochastic Volatility Models: Conditional Normality Versus Heavy-Tailed Distributions , 1997 .

[23]  Peter E. Rossi,et al.  Bayesian analysis of stochastic volatility models with fat-tails and correlated errors , 2004 .

[24]  P. Cerqueira,et al.  Causes of the Decline of Economic Growth in Italy and the Responsibility of EURO. A Balance-of-Payments Approach , 2012 .

[25]  M. Pitt,et al.  Likelihood analysis of non-Gaussian measurement time series , 1997 .

[26]  N. Shephard,et al.  Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns , 1996 .

[27]  Georgios Tsiotas.  On generalised asymmetric stochastic volatility models , 2012, Comput. Stat. Data Anal..

[28]  Siddhartha Chib,et al.  MARKOV CHAIN MONTE CARLO METHODS: COMPUTATION AND INFERENCE , 2001 .

[29]  Micaela Antunes,et al.  The Effects of Internal and External Imbalances on Italy´s Economic Growth. A Balance of Payments Approach with Relative Prices No Neutral , 2013 .

[30]  N. Shephard,et al.  Stochastic volatility with leverage: Fast and efficient likelihood inference , 2007 .

[31]  Leonel Sousa,et al.  Parallel LDPC Decoding , 2011 .

[32]  Murali Haran,et al.  Parallel multivariate slice sampling , 2011, Stat. Comput..

[33]  Christian P. Robert,et al.  Using Parallel Computation to Improve Independent Metropolis–Hastings Based Estimation , 2010, ArXiv.

[34]  S. Chib,et al.  Multivariate stochastic volatility , 2009 .