Bayesian inference for a single factor copula stochastic volatility model using Hamiltonian Monte Carlo

Abstract

For modeling multivariate financial time series a single factor copula model with stochastic volatility margins is proposed. It generalizes single factor models based on the multivariate normal distribution by allowing for symmetric and asymmetric tail dependence. A joint Bayesian approach using Hamiltonian Monte Carlo (HMC) within Gibbs sampling is developed. Thus, the information loss caused by the two-step approach for margins and dependence is avoided. Further, the Bayesian approach is tractable in high dimensional parameter spaces in addition to uncertainty quantification through credible intervals. By introducing indicators for different copula families the copula families are selected automatically in the Bayesian framework. In a first simulation study the performance of HMC for the copula part is compared to a procedure based on adaptive rejection Metropolis sampling within Gibbs sampling. It is shown that HMC considerably outperforms this alternative approach in terms of effective sample size per minute. In a second simulation study satisfactory performance is seen for the full HMC within Gibbs procedure. The approach is illustrated for a portfolio of financial assets with respect to one-day ahead value at risk forecasts. Comparison to a two-step estimation procedure and to relevant benchmark models, such as a multivariate factor stochastic volatility model, shows superior performance of the proposed approach.