An Empirical Analysis of Oil and Stock Markets’ Volatility Based on the DGC-MSV-t Model

We investigate the spillover effect between crude oil future prices, crude oil spot prices, and stock index by using the multivariate stochastic volatility model. These tests between each market show the significant Granger causes of spillover effect. More and more evidences show that the crude oil price has been affected by other financial markets. The oil future played an important role in the energy market. WTI and Brent oil future have more spillover effect than INE oil future. The result shows that S&P stock market is more sensitive to the oil price than Shanghai stock market. The cross-market spillover effect we found can give some advices for the investor of oil and stock market. DIC test shows that DGC-MSV-t is considered effective and more accurate.

“Exact” and Approximate Methods for Bayesian Inference: Stochastic Volatility Case Study

We conduct a case study in which we empirically illustrate the performance of different classes of Bayesian inference methods to estimate stochastic volatility models. In particular, we consider how different particle filtering methods affect the variance of the estimated likelihood. We review and compare particle Markov Chain Monte Carlo (MCMC), RMHMC, fixed-form variational Bayes, and integrated nested Laplace approximation to estimate the posterior distribution of the parameters. Additionally, we conduct the review from the point of view of whether these methods are (1) easily adaptable to different model specifications; (2) adaptable to higher dimensions of the model in a straightforward way; (3) feasible in the multivariate case. We show that when using the stochastic volatility model for methods comparison, various data-generating processes have to be considered to make a fair assessment of the methods. Finally, we present a challenging specification of the multivariate stochastic volatility model, which is rarely used to illustrate the methods but constitutes an important practical application.

New Estimators of the Bayes Factor for Models with High-Dimensional Parameter and/or Latent Variable Spaces

Formal Bayesian comparison of two competing models, based on the posterior odds ratio, amounts to estimation of the Bayes factor, which is equal to the ratio of respective two marginal data density values. In models with a large number of parameters and/or latent variables, they are expressed by high-dimensional integrals, which are often computationally infeasible. Therefore, other methods of evaluation of the Bayes factor are needed. In this paper, a new method of estimation of the Bayes factor is proposed. Simulation examples confirm good performance of the proposed estimators. Finally, these new estimators are used to formally compare different hybrid Multivariate Stochastic Volatility–Multivariate Generalized Autoregressive Conditional Heteroskedasticity (MSV-MGARCH) models which have a large number of latent variables. The empirical results show, among other things, that the validity of reduction of the hybrid MSV-MGARCH model to the MGARCH specification depends on the analyzed data set as well as on prior assumptions about model parameters.

Cross-Market Infection Research on Stock Herding Behavior Based on DGC-MSV Models and Bayesian Network

This paper is concerned with the multivariate stochastic volatility modeling of the stock market. We investigate a DGC-t-MSV model to find the historical volatility spillovers between nine markets, including S&P, Nasdaq, SSE, SZSE, HSI, FTSE, CAC, DAX, and Nikkei indices. We use the Bayesian network to analyze the spreading of herd behavior between nine markets. The main results are as follows: (1) the DGC-t-MSV model we considered is a useful way to estimate the parameter and fit the data well in the stock market; (2) our computational analysis shows that the S&P and Nasdaq have higher volatility spillovers to the Shanghai and Shenzhen stock markets; (3) the results also show that there is a strong correlation between stock markets in the same region.

Dynamic Correlation Multivariate Stochastic Volatility Black-Litterman With Latent Factors

In finance, it is often of interest to study market volatility for portfolios that may consist of a large number of assets using multivariate stochastic volatility models. However, such models, though useful, do not usually incorporate investor views that might be available. In this paper we introduce a novel hierarchical Bayesian methodology of modeling volatility for a large portfolio of assets that incorporates investor’s personal views of the market via the Black-Litterman (BL) model. We extend the scope and use of BL models by using it within a multivariate stochastic volatility model based on latent factors for dimensionality reduction but allows for time varying correlations. Detailed derivations of MCMC algorithm are provided with an illustration with S&P500 asset returns. Moreover, sensitivity analysis for the confidence levels that the investor has in their personal views is also explored. Numerical results show that the proposed method provides flexible interpretation based on the investor’s uncertainty in personal beliefs, and converges to the empirical sample estimate when their confidence level of the market becomes weak.

Bayesian Analysis of Additive Factor Volatility Models with Heavy-Tailed Distributions with Specific Reference to S&P 500 and SSEC Indices1

The distribution of the financial return series is unsuitable for normal distribution. The distribution of financial series is heavier than the normal distribution. In addition, parameter estimates obtained in the presence of outliers are unreliable. Therefore, models that allow heavy-tailed distribution should be preferred for modelling high kurtosis. Accordingly, univariate and multivariate stochastic volatility models, which allow heavy-tailed distribution, have been proposed to model time-varying volatility. One of the multivariate stochastic volatility (MSVOL) model structures is factor-MSVOL model. The aim of this study is to investigate the convenience of Bayesian estimation of additive factor-MSVOL (AFactor-MSVOL) models with normal, heavy-tailed Student-t and Slash distributions via financial return series. In this study, AFactor-MSVOL models that allow normal, Student-t, and Slash heavy-tailed distributions were estimated in the analysis of return series of S&P 500 and SSEC indices. The normal, Student-t, and Slash distributions were assigned to the error distributions as the prior distributions and full conditional distributions were obtained by using Gibbs sampling. Model comparisons were made by using DIC. Student-t and Slash distributions were shown as alternatives of normal AFactor-MSVOL model.