Bayesian Analysis of a Stochastic Volatility Model with Leverage Effect and Fat Tails
Boston University School of Management; HEC Montreal - Department of Finance
Peter E. Rossi
University of California, Los Angeles (UCLA) - Anderson School of Management
University of Chicago - Booth School of Business
Boston College Finance Dept. Working Paper
The basic univariate stochastic volatility model specifies that conditional volatility follows a log-normal auto-regressive model with innovations assumed to be independent of the innovations in the conditional mean equation. Since the introduction of practical methods for inference in the basic volatility model (JPR-(1994)), it has been observed that the basic model is too restrictive for many financial series. We extend the basic SVOL to allow for a so-called "Leverage effect" via correlation between the volatility and mean innovations, and for fat-tails in the mean equation innovation. A Bayesian Markov Chain Monte Carlo algorithm is developed for the extended volatility model. Thus far, likelihood-based inference for the correlated SVOL model has not appeared in the literature. We develop Bayes Factors to assess the importance of the leverage and fat-tail extensions. Sampling experiments reveal little loss in precision from adding the model extensions but a large loss from using the basic model in the presence of mis-specification. For both equity and exchange rate data, there is overwhelming evidence in favor of models with fat-tailed volatility innovations, and for a leverage effect in the case of equity indices. We also find that volatility estimates from the extended model are markedly different from those produced by the basic SVOL.
Number of Pages in PDF File: 31
Keywords: ARCH, Bayes factor, Fat-tails, Gibbs Leverage effect, Metropolis, MCMC, Stochastic volatility
JEL Classification: C1, C11, C15, G1
Date posted: July 16, 2001
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