Research On Jump Dynamics In Stock Market Returns Based On Regime Switching ARJI Model

As a basic theory of portfolio optimization, risk management and other investment activities in the capital markets, the behavior of stock market returns has been a research emphasis for a long time. Recently, the global financial situation has frequently fluctuated, all kinds of emergencies have happened, which have made stock market returns jump severely. Under this realistic background, the jump behavior of stock market returns becomes a hot area and constructing an adequate model is the core of this issue. In view of current research deficiencies, we take the regime switching process and the jump process together into consideration and construct regime switching ARJI models to investigate the jump behavior.First of all, we comprehensively review and analyze the related theories and methods of the jump behavior and the regime switching process, then propose a regime switching jump diffusion stochastic differential equation by introducing Markov regime switching process into the basic jump diffusion stochastic differential equation, and construct regime switching ARJI models. At last, check the ability of the constructed models on data fitting, jump behavior identification and prediction.An empirical analysis of SSE Composite Index from Mar.72002to Aug.82013indicates that there are two distinctly different regimes, namely the high volatility regime and the low volatility regime in China’s stock market. The jump behavior of SSE Composite Index returns features dynamics and exhibits leverage effect, and varies largely form regime to regime. The jump size mean is time-varing and of leverage effect, and large in the high volatility regime. China’s stock market is mainly controlled by bad news in the high volatility regime, but by good news in the low volatility regime. The jump size variance is of no dynamics, and large in the high volatility regime than that in the low volatility regime. The jump intensity is time-varing in both regime, but lasts longer in the high volatility regime. The average jump risk in the high volatility regime is about2.5times as large as that in the low volatility regime. In addition, we also find that the regime switching ARJI models perform better than the GARCH models and the ARJI models on data fitting and jump behavior measurement.