随机跳变广义双指数分布下的双重跳跃扩散模型及应用

结合非对称双指数分布与有偏双指数分布构建了广义双指数分布,该分布能充分展现金融市场的有偏、非对称与尖峰厚尾特征. 借鉴Kou提出的双指数跳跃扩散模型,构建和分析了广义双指数分布下的单层跳跃扩散模型(GDED-KDJ),考虑到金融序列的异方差性与波动跳跃性,参考Eraker提出的双重跳跃扩散模型, 进一步将GDED-KDJ模型扩展为随机跳变广义双指数分布下的双重跳跃扩散模型,分析了新模型具备的一般性、有偏性、非对称性与尖峰厚尾性,进而从理论上证明了新模型的优越性. 同时,还研究了新模型的条件似然函数及MCMC迭代求解算法.最后,利用金融危机期间我国主要三种金属期货价格的三月连 续数据进行实证,结果也进一步表明新模型的可行性、有效性与优越性.

Double-jump diffusion model based on the generalized double exponential distribution of the random jump and its application

The generalized double exponential distribution is proposed by combining the asymmetric and biased double exponential distributions, which could fully disclose the features of bias, asymmetry, and steep-peak and heavy tails in financial markets. By referencing to the KDJ model, the generalized double exponential jump diffusion model (GDED-KDJ) is proposed and analyzed. Taking into account the heteroskedasticity and volatility jump, and the double jump diffusion model proposed by Eraker, we further extend the GDED-KDJ to the generalized double exponential double-jump diffusion model, i.e., GDED-SVIJ model. Then, we analyze the features of the new model, such as the general, biased, asymmetric and steep-peak and heavy tails, which also present its superiority. Also, we study the conditions likelihood function and MCMC iterative algorithm of the new model. At last, by the empirical study about three metal futures in SHEF, the feasibility and superiority of the new model are showed and proved.