"Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student's t-Distribution Models"

Bayesian analysis of a stochastic volatility model with a generalized hyperbolic (GH) skew Student's t-error distribution is described where we first consider an asymmetric heavy-tailed error and leverage effects. An efficient Markov chain Monte Carlo estimation method is described that exploits a normal variance-mean mixture representation of the error distribution with an inverse gamma distribution as the mixing distribution. The proposed method is illustrated using simulated data, daily S&P500 and TOPIX stock returns. The models for stock returns are compared based on the marginal likelihood in the empirical study. There is strong evidence in the stock returns high leverage and an asymmetric heavy-tailed distribution. Furthermore, a prior sensitivity analysis is conducted whether the results obtained are robust with respect to the choice of the priors.

"Block Sampler and Posterior Mode Estimation for Asymmetric Stochastic Volatility Models"

This article introduces a new efficient simulation smoother and disturbance smoother for asymmetric stochastic volatility models where there exists a correlation between today's return and tomorrow's volatility. The state vector is divided into several blocks where each block consists of many state variables. For each block, corresponding disturbances are sampled simultaneously from their conditional posterior distribution. The algorithm is based on the multivariate normal approximation of the conditional posterior density and exploits a conventional simulation smoother for a linear and Gaussian state space model. The performance of our method is illustrated using two examples (1) simple asymmetric stochastic volatility model and (2) asymmetric stochastic volatility model with state-dependent variances. The popular single move sampler which samples a state variable at a time is also conducted for comparison in the first example. It is shown that our proposed sampler produces considerable.

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.

Block Sampler and Posterior Mode Estimation for Asymmetric Stochastic Volatility Models (Published in "Computational Statistics and Data Analysis", 52-6, 2892-2910. February 2008. )

This article introduces a new efficient simulation smoother and disturbance smoother for asymmetric stochastic volatility models where there exists a correlation between today`s return and tomorrow`s volatility. The state vector is divided into several blocks where each block consists of many state variables. For each block, corresponding disturbances are sampled simultaneously from their conditional posterior distribution. The algorithm is based on the multivariate normal approximation of the conditional posterior density and exploits a conventional simulation smoother for a linear and Gaussian state space model. The performance of our method is illustrated using two examples (1) simple asymmetric stochastic volatility model and (2) asymmetric stochastic volatility model with state-dependent variances. The popular single move sampler which samples a state variable at a time is also conducted for comparison in the first example. It is shown that our proposed sampler produces considerable improvement in the mixing property of the Markov chain Monte Carlo chain.

Stochastic Volatility Model with Leverage and Asymmetrically Heavy-tailed Error Using GH Skew Student's t-distribution

Bayesian analysis of a stochastic volatility model with a generalized hyperbolic (GH) skew Student's t-error distribution is described where we first consider an asymmetric heavy-tailness as well as leverage effects. An efficient Markov chain Monte Carlo estimation method is described exploiting a normal variance-mean mixture representation of the error distribution with an inverse gamma distribution as a mixing distribution. The proposed method is illustrated using simulated data, daily TOPIX and S&P500 stock returns. The model comparison for stock returns is conducted based on the marginal likelihood in the empirical study. The strong evidence of the leverage and asymmetric heavy-tailness is found in the stock returns. Further, the prior sensitivity analysis is conducted to investigate whether obtained results are robust with respect to the choice of the priors.generalized hyperbolic skew Student's t-distribution, Markov chain Monte Carlo, Mixing distribution, State space model, Stochastic volatility, Stock 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.

Block Sampler and Posterior Mode Estimation for A Nonlinear and Non-Gaussian State-Space Model with Correlated Errors

This article introduces a new efficient simulation smoother and disturbance smoother for general state-space models where there exists a correlation between error terms of the measurement and state equations. The state vector is divided into several blocks where each block consists of many state variables. For each block, corresponding disturbances are sampled simultaneously from their conditional posterior distribution. The algorithm is based on the multivariate normal approximation of the conditional posterior density and exploits a conventional simulation smoother for a linear and Gaussian state space model. The performance of our method is illustrated using two examples (1) stochastic volatility models with leverage effects and (2) stochastic volatility models with leverage effects and state-dependent variances. The popular single move sampler which samples a state variable at a time is also conducted for comparison in the first example. It is shown that our proposed sampler produces considerable improvement in the mixing property of the Markov chain Monte Carlo chain.

"Leverage, heavy-tails and correlated jumps in stochastic volatility models"

This paper proposes the efficient and fast Markov chain Monte Carlo estimation methods for the stochastic volatility model with leverage effects, heavy-tailed errors and jump components, and for the stochastic volatility model with correlated jumps. We illustrate our method using simulated data and analyze daily stock returns data on S&P500 index and TOPIX. Model comparisons are conducted based on the marginal likelihood for various SV models including the superposition model.