广义双指数分布的跳跃扩散模型下股指期货波动研究

Research on Stock Index Futures Volatility under Generalized Double Exponential Distribution Jump Diffusion Model

金融期货市场既存在平常信息引起的连续性波动,又存在突发冲击造成的跳跃式波动,金融市场波动同时具有扩散性和跳跃性特点。同时,金融期货市场与现货市场间的跳跃和波动行为存在着风险溢出效应和羊群效应等。并且,金融资产收益在跳跃过程中呈现出非高斯属性,正态分布假设不能刻画跳跃和波动中的程式化现象,如噪音分布的尖峰厚尾、有偏特征等。考虑到金融期货序列分布的尖峰厚尾、有偏、非对称现象,采用非对称、有偏的广义双指数分布刻画收益率非高斯特征;同时考虑到金融波动序列的时变性、集聚性和异方差性以及收益与波动之间存在着杠杆效应,将有偏的广义双指数分布引入到收益序列和波动序列均存在跳跃且跳跃相关的双层跳跃扩散模型,构建广义双指数分布驱动的双层跳跃扩散模型,并从理论上分析模型的优越性。根据模型的似然函数估计式,使用马尔科夫链蒙特卡洛模拟迭代求解广义双指数分布驱动的双层跳跃扩散模型参数,将构建的模型应用到中国股指期货和现货市场进行实证研究,分析中国股指期货和现货市场各自的跳跃和波动行为特征以及市场间跳跃和波动的风险关联性,包括对两类市场跳跃形态的非高斯特征分析股指期货市场与现货指数的波动协同性描述,以及股指期货与现货间的跳跃溢出行为、跳跃强度和跳跃大小分析等。研究结果表明,广义双指数分布驱动的双层跳跃扩散模型较好地捕获了收益率分布的尖峰厚尾特征;股指期货收益和股指现货收益上涨与下跌概率呈现非对称性;股指期货波动强度高于股指现货波动,而股指期货波动的持久性低于股指现货;股指现货的杠杆效应表现更强;股指期货和股指现货市场存在双向跳跃溢出效应。研究结论有利于理解中国沪深300股指期货市场和现货市场之间的跳跃风险传染机制,对于深入认识期货和现货市场的风险溢出关系、促使投资者规避风险和监管机构加强监管具有一定的参考作用。

There are both continuous volatility caused by the usual information and the jumping volatility caused by the sudden impact in financial futures market. And the financial market volatility exhibits both diffusive and jumping characteristics. At the same time,there are spillover risks and flock effects in the jump and volatility behavior between the financial futures market and spot market. In addition,the returns of financial assets jumps show non-Gaussian properties,and the normal distribution assumption cannot describe the stylized phenomenon（ the leptokurtic,skewed and asymmetric phenomena in noise distribution） in jumping and volatility.Considering the leptokurtic,skewed and asymmetric phenomena in the financial futures distribution,the asymmetric and biased generalized double exponential distribution（ GDED） is used to characterize the non-Gaussian features of the returns. Taking into account the time-varying,clustering property and heteroscedasticity of financial volatility sequence,and the leverage effects between returns and volatility,the generalized double exponential distribution is introduced into the double-layer jump diffusion（ SVCJ） model in which the returns series and volatility series both exist relevant jumps,thus constructing the GDED-SVCJ. This jump diffusion model is driven by GDED distribution and we theoretically analyzed the superiority of the model. According to the derived likelihood function estimation expression of the model,the GDED-SVCJ parameters are solved by using the Markov chain Monte Carlo（ MCMC） simulation.And the newly constructed model is applied to the financial futures market and spot market of China for empirical researches. The jump and volatility behavioral characteristics,inter-market jump and volatility risk relevance are analyzed,which include the non-Gaussian feature analysis of two types of market jumps,the synchronic description of the stock index futures and spot,and the jump spillover behaviors,jump intensity and jump size analysis between stock futures and index.The empirical studies show that the GDED-SVCJ model captures the leptokurtic and thick tail characteristics of the returns distribution well. The rise and fall probability of futures returns and the spot index returns are asymmetric. The futures volatile intensity is higher than the index volatility,while the persistence of stock index futures volatility is relatively lower than that of the spot index,with the stock index has stronger leverage effect. The stock index futures and spot market display two-way jump spillover effects.The conclusion contributes to the understanding of risk transmission mechanism and the risk spillover correlation of the financial stock index futures market and the stock index spot market,as well as helping investors to avoid risks and strengthen supervision of supervisors.