Markov chain Monte Carlo and data augmentation methods for continuous-time stochastic volatility models

                         Witte, Hugh Douglas; PhD

                         THE UNIVERSITY OF ARIZONA, 1999
                         ECONOMICS, FINANCE (0508); STATISTICS (0463)

                         In this paper we exploit some recent computational advances in Bayesian inference, coupled with data
                         augmentation methods, to estimate and test continuous-time stochastic volatility models. We augment
                         the observable data with a latent volatility process which governs the evolution of the data's volatility. The
                         level of the latent process is estimated at finer increments than the data are observed in order to derive a
                         consistent estimator of the variance over each time period the data are measured. The latent process
                         follows a law of motion which has either a known transition density or an approximation to the transition
                         density that is an explicit function of the parameters characterizing the stochastic differential equation.
                         We analyze several models which differ with respect to both their drift and diffusion components. Our
                         results suggest that for two size-based portfolios of U.S. common stocks, a model in which the volatility
                         process is characterized by nonstationarity and constant elasticity of instantaneous variance (with respect
                         to the level of the process) greater than 1 best describes the data. We show how to estimate the various
                         models, undertake the model selection exercise, update posterior distributions of parameters and
                         functions of interest in real time, and calculate smoothed estimates of within sample volatility and
                         prediction of out-of-sample returns and volatility. One nice aspect of our approach is that no
                         transformations of the data or the latent processes, such as subtracting out the mean return prior to
                         estimation, or formulating the model in terms of the natural logarithm of volatility, are required.


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