连续时间金融框架下证券市场跳跃模型研究

The Research of Jump Models in Equity Market under the Framework of Continuous-time Finance

为了准确刻画证券的价格和波动过程中的跳跃特征,文章采用基于贝叶斯分析的马尔可夫链蒙特卡罗(MCMC)模拟方法,利用离散样本数据,分别分析了连续时间内,收益与波动过程存在相关无限活跃列维跳跃的随机波动模型以及仿射跳跃扩散模型(AJD)。首先,MCMC方法可以准确联合估计模型中扩散、随机波动以及列维跳跃各个成分的特征参数;其次,与仿射跳跃扩散模型相比,无限活跃列维跳跃的随机波动模型可以捕捉到在收益与波动过程中,那些由布朗运动和复合泊松过程所不能刻画的列维跳跃,从而更好地描述金融时间序列的动态特征。最后,通过对中国上证综合指数收益序列的实证研究,验证了上述结论。

In order to characterize the jump features of securities prices and volatility processes, this paper developed Markov chain Monte Carlo （MCMC） simulation methods based on Bayesian analysis for inferences of continuous-time models with stochastic volatility and infinite-activity Levy jumps and the affine jump-diffusion model using discretely sampled data. First of all, MCMC methods can be accurately joint estimated of diffusion, stochastic volatility, and Levy jump. Second, compared with the affine jump-diffusion model, stochastic volatility with infinite-activity Levy jumps model can captured the Levy jumps which are the Brownian motion and compound Poisson process can not characterize, thus it is better to describe the characteristics of the dynamic time series. Finally, empirical studies on China＇s Shanghai Composite Index sequence of return show those conclusions mentioned above.