跳跃扩散Cox-Ingersoll-Ross利率模型  

Jump-diffusion Cox-Ingersoll-Ross model

作　　者：盛洁 闫理坦[1] SHENG Jie;YAN Litan(College of Science,Donghua University,Shanghai 201620,China)

机构地区：[1]东华大学理学院,上海201620

出　　处：《苏州科技大学学报（自然科学版）》2018年第1期33-38,共6页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11571071)

摘　　要：在经典的时齐短期利率模型中,Cox-Ingersoll-Ross模型在Vasicek的基础上在扩散系数中加入了平方根项,从而保证了它的瞬时短期利率始终为正,这与Vasicek模型相比更符合利率的实际情况。而为了更准确地描述利率数据变化的随机现象,该文着重研究的是带跳的Cox-Ingersoll-Ross模型。在经过对该模型的过程路径进行Monte Carlo数值模拟,同时实现特征函数的Laplace逆变换后,通过有效的数值方法近似转移密度函数从而有效地逼近似然函数,并在此基础上对跳跃扩散Cox-Ingersoll-Ross利率模型参数做贝叶斯估计,取得了良好结果。In classical time-homogeneous short-rate models,the model developed by Cox,Ingersoll and Ross added square-root term in the diffusion coefficient of the dynamics proposed by Vasicek,which ensures that the instantaneous short rate is always positive.In order to draw a better picture of the stochastic changes of the real-world interest rates,we mainly discussed the jump diffusion Cox-Ingersoll-Ross model.Using the Monte Carlo numerical simulation method to simulate the jump diffusion path of this model and approaching the Laplace Inversion of the characteristic function,we implemented effective numerical approximation over transition density function and likelihood function.Based on this,we made the Bayesian estimation of the jump-diffusion Cox-Ingersoll-Ross model and ultimately achieved good results.

关 键 词：利率 Cox-Ingersoll-Ross模型 跳跃扩散随机过程 LAPLACE逆变换 MONTE Carlo 贝叶斯估计 

分 类 号：O211.4[理学—概率论与数理统计]