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.

A Bayesian Semiparametric Realized Stochastic Volatility Model

This paper proposes a semiparametric realized stochastic volatility model by integrating the parametric stochastic volatility model utilizing realized volatility information and the Bayesian nonparametric framework. The flexible framework offered by Bayesian nonparametric mixtures not only improves the fitting of asymmetric and leptokurtic densities of asset returns and logarithmic realized volatility but also enables flexible adjustments for estimation bias in realized volatility. Applications to equity data show that the proposed model offers superior density forecasts for returns and improved estimates of parameters and latent volatility compared with existing alternatives.

The Log-Asset Dynamic with Euler–Maruyama Scheme under Wishart Processes

This article deals with Wishart process which is defined as matrix generalization of a squared Bessel process. We consider a single risky asset pricing model whose volatility is described by Wishart affine diffusion processes. The multifactor volatility specification enables this model to be flexible enough to describe the market prices for short or long maturities. The aim of the study is to derive the log-asset returns dynamic under the double Wishart stochastic volatility model. The corrected Euler–Maruyama discretization technique is applied in order to obtain the numerical solution of the log-asset return dynamic under Bi-Wishart processes. The numerical examples show the effect of the model parameters on the asset returns under the double Wishart volatility model.

An Efficient Numerical Scheme for the Solution of a Stochastic Volatility Model Including Contemporaneous Jumps in Finance

The model of stochastic volatility with contemporaneous jumps is written for pricing under a partial integro-differential equation (PIDE) having a double integral and a nonsmooth initial value. To tackle this problem, first, a new radial basis function (RBF) as a convex combination of two known RBFs is given. Second, the weighting coefficients of the RBF generated finite difference (FD) method are contributed and the associated error equations are derived. To deal with the integral part, the new idea is to apply an estimate for the unknown function for every cell and do an integration of the density function. The contributed approach is competitive and reduces both the calculational efforts and elapsed time.

Option pricing under the fractional stochastic volatility model

We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented. doi:10.1017/S1446181121000225