Large Movement of Market and Risk Control Strategy For Index futures Based on Levy Process

Recently, a number of papers provide compelling evidence to the significant existence of large movement in capital market. Such large movement of market usually exhibits an abrupt jump, upwards or downward, in the price of financial asset, along with inducing a particular risk to investors. In order to explore this market behavior more clearly, we propose a Levy type model in this paper to model the change of stock index. Unlike many other jump or diffusion stochastic volatility models, our model provides a channel through which jump dynamics and volatility can display an interactive influence on each other. Based on the model, we then discuss a VaR risk control strategy for index futures. The empirical results indicate the significant existence of large movements in China stock market and their great impact on index return and volatility. Hence, it is important for us to take them into accounting when pricing index futures or making portfolio decision. Our results also support the assumption of an interactive relationship between volatility and jump dynamics. Meanwhile, conventional ARCH type models, such as GJR-GARCH, are definitely misspecified, since they significantly overshoot the index volatility after a large movement of the market. Overall, our results provide a more profound understanding on large movement or jumps in market, and a new way of modeling and forecasting of volatility as well as the risk control of index futures.