Dynamic Hedging Based on Markov Regime-Switching Dynamic Correlation Multivariate Stochastic Volatility Model

It is important to consider the changing states in hedging.The Markov regime-switching dynamic correlation multivariate stochastic volatility( MRS-DC-MSV) model was proposed to solve this issue. DC-MSV model and MRS-DC-MSV model were used to calculate the time-varying hedging ratios and compare the hedging performance. The Markov chain Monte Carlo( MCMC) method was used to estimate the parameters. The results showed that,there were obviously two economic states in Chinese financial market. Two models all did well in hedging,but the performance of MRS-DCMSV model was better. It could reduce risk by nearly 90%. Thus,in the hedging period,changing states is a factor that cannot be neglected.

Properties of Time-Varying Causality Tests in the Presence of Multivariate Stochastic Volatility

This paper compares the statistical properties of time-varying causality tests when errors of variables have multivariate stochastic volatility (SV). The time-varying causal-ity tests in this paper are based on a logistic smooth transition autoregressive model. The compared time-varying causality tests include asymptotic tests, heteroskedasticity-robust tests, and tests using wild bootstrap. Our simulation results show that asymptotic tests and heteroskedasticity-robust counterparts have size distortions under multivariate SV, whereas tests using wild bootstrap have better size properties regardless of type of error. In particular, the time-varying causality test with first-order Taylor approximation using wild bootstrap has better statistical properties.

Performance analysis of stochastic gradient algorithms under weak conditions

By using the stochastic martingale theory, convergence properties of stochastic gradient （SG） identification algorithms are studied under weak conditions. The analysis indicates that the parameter estimates by the SG algorithms consistently converge to the true parameters, as long as the information vector is persistently exciting （i.e., the data product moment matrix has a bounded condition number） and that the process noises are zero mean and uncorrelated. These results remove the strict assumptions, made in existing references, that the noise variances and high-order moments exist, and the processes are stationary and ergodic and the strong persis- tent excitation condition holds. This contribution greatly relaxes the convergence conditions of stochastic gradient algorithms. The simulation results with bounded and unbounded noise variances confirm the convergence conclusions proposed.

Two-component Brownian coagulation: Monte Carlo simulation and process characterization

The compositional distribution within aggregates of a given size is essential to the functionality of com- posite aggregates that are usually enlarged by rapid Brownian coagulation, There is no analytical solution for the process of such two-component systems, Monte Carlo method is an effective numerical approach for two-component coagulation, In this paper, the differentially weighted Monte Carlo method is used to investigate two-component Brownian coagulation, respectively, in the continuum regime, the free-molecular regime and the transition regime. It is found that （1） for Brownian coagulation in the continuum regime and in the free-molecular regime, the mono-variate compositional distribution, i.e., the number density distribution function of one component amount （in the form of volume of the component in aggregates） satisfies self-preserving form the same as particle size distribution in mono-component Brownian coagulation; （2） however, for Brownian coagulation in the transition regime the mono-variate compositional distribution cannot reach self-similarity; and （3） the bivariate compositional distribution, i.e., the combined number density distribution function of two component amounts in the three regimes satisfies a semi self-preserving form. Moreover, other new features inherent to aggregative mixing are also demonstrated; e.g., the degree of mixing between components, which is largely controlled by the initial compositional mass fraction, improves as aggregate size increases.