Efficient Bayesian Estimation of a Multivariate Stochastic Volatility Model with Cross Leverage and Heavy-Tailed Errors

An efficient Bayesian estimation using a Markov chain Monte Carlo method is proposed in the case of a multivariate stochastic volatility model as a natural extension of the univariate stochastic volatility model with leverage and heavy-tailed errors. Note that we further incorporate cross-leverage effects among stock returns. Our method is based on a multi-move sampler that samples a block of latent volatility vectors. The method is presented as a multivariate stochastic volatility model with cross leverage and heavytailed errors. Its high sampling efficiency is shown using numerical examples in comparison with a single-move sampler that samples one latent volatility vector at a time, given other latent vectors and parameters. To illustrate the method, empirical analyses are provided based on five-dimensional S&P500 sector indices returns.

"Efficient Bayesian Estimation of a Multivariate Stochastic Volatility Model with Cross Leverage and Heavy-Tailed Errors"

An efficient Bayesian estimation using a Markov chain Monte Carlo method is proposed in the case of a multivariate stochastic volatility model as a natural extension of the univariate stochastic volatility model with leverage and heavy-tailed errors. Note that we further incorporate cross-leverage effects among stock returns. Our method is based on a multi-move sampler that samples a block of latent volatility vectors. The method is presented as a multivariate stochastic volatility model with cross leverage and heavytailed errors. Its high sampling efficiency is shown using numerical examples in comparison with a single-move sampler that samples one latent volatility vector at a time, given other latent vectors and parameters. To illustrate the method, empirical analyses are provided based on five-dimensional S&P500 sector indices returns.

Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors

The efficient Bayesian estimation method using Markov chain Monte Carlo is proposed for a multivariate stochastic volatility model that is a natural extension of the univariate stochastic volatility model with leverage and heavy-tailed errors, where we further incorporate cross leverage effects among stock returns. Our method is based on a multi-move sampler which samples a block of latent volatility vectors and is described first in the literature for a multivariate stochastic volatility model with cross leverage and heavy-tailed errors. Its high sampling efficiency is shown using numerical examples in comparison with a single-move sampler which samples one latent volatility vector at a time given other latent vectors and parameters. The empirical studies are given using five dimensional stock return indices in Tokyo Stock Exchange.

Markov Switching Asymmetric Stochastic Volatility Model with Application to TOPIX Data -A Permutation Sampler Approach-

The stochastic volatility model has been popular to explain a dynamic structure of financial time series such asset returns. In this paper, we first consider the asymmetry that the increase in the volatility is followed by the decrease in the asset return. Then, we consider a Markov switching of two (high and low) volatility states using a random state variable which follows a Markov process. The restrictions for the identification of the switching parameters are determined by using a permutation sampler with Markov chain Monte Carlo method. The Markov switching asymmetric stochastic volatility model is applied to TOPIX returns data, and model comparisons are conducted.

"Markov Switching Asymmetric Stochastic Volatility Model with Application to TOPIX Data -A Permutation Sampler Approach-"(in Japanese)

The stochastic volatility model has been popular to explain a dynamic structure of financial time series such asset returns. In this paper, we first consider the asymmetry that the increase in the volatility is followed by the decrease in the asset return. Then, we consider a Markov switching of two (high and low) volatility states using a random state variable which follows a Markov process. The restrictions for the identification of the switching parameters are determined by using a permutation sampler with Markov chain Monte Carlo method. The Markov switching asymmetric stochastic volatility model is applied to TOPIX returns data, and model comparisons are conducted.

Matrix Exponential Stochastic Volatility with Cross Leverage

A multivariate stochastic volatility model with the dynamic correlation and the cross leverage effect is described and its efficient estimation method using Markov chain Monte Carlo is proposed. The time-varying covariance matrices are guaranteed to be positive definite by using a matrix exponential transformation. Of particular interest is our approach for sampling a set of latent matrix logarithm variables from their conditional posterior distribution, where we construct the proposal density based on an approximating linear Gaussian state space model. The proposed model and its extended models with fat-tailed error distribution are applied to trivariate returns data (daily stocks, bonds, and exchange rates) of Japan. Further, a model comparison is conducted including constant correlation multivariate stochastic volatility models with leverage

Matrix Exponential Stochastic Volatility with Cross Leverage

A multivariate stochastic volatility model with dynamic correlation and leverage effect is described and estimated. The matrix exponential transformation is used to keep the time-varying covariance matrices positive definite. An efficient Bayesian estimation method using Markov chain Monte Carlo is proposed. Of particular interest is our approach for sampling the latent state variables from the conditional posterior distribution, using a blocked multi-move Metropolis-Hastings sampling, in which the proposal density is derived from an approximating linear Gaussian state space model. The proposed model is applied to the daily stock price index, the Japanese bond price index, and the Yen/USD exchange rate returns data