马氏转移高敏感跳扩散CKLS模型的解及金融应用  

Solutions of highly sensitive jump-diffusion CKLS model under Markovian switching and applications in finance

作　　者：陈惠达 尹居良 CHEN Huida;YIN Juliang(Department of Statistics,Jinan University,Guangzhou 510632,China;Department of Statistics,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]暨南大学统计学系,广州510632 [2]广州大学统计学系,广州510006

出　　处：《系统工程理论与实践》2018年第9期2212-2229,共18页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(61573006)~~

摘　　要：将马氏转移切换机制和泊松过程引入到CKLS短期利率模型中,构建马氏转移跳扩散CKLS模型.理论方面,利用Lyapunov函数方法证明了马氏转移跳扩散CKLS模型存在唯一的全局正解并给出了该解的分析性质（包括一阶矩二阶矩的有界性,随机有界性和路径估计）;用欧拉离散化方法得到马氏转移跳扩散CKLS模型的欧拉数值解,证明了其依概率收敛于解析解.应用方面,以债券定价和障碍期权的期望收益为例给出了马氏转移跳扩散CKLS模型数值解的收敛性在金融领域中的应用.基于7天Shibor利率的实证分析,说明了马氏转移跳扩散CKLS模型对我国金融市场中动态利率建模更加合理和有效.This paper establishes a jump-diffusion CKLS model under Markovian switching via incorporating Markovian switching and Poisson process into CKLS short-term interest rate model. In theory, by using Lyapunov function method, the existence and uniqueness of global positive solution of jump-diffusion CKLS model under Markovian switching are proved and analytical properties of the solution including the boundedness of its first-order and second-order moments, stochastic boundedness and path estimation are given. By using Euler-Maruyama discretization method, numerical solutions of such a model are derived,and it is shown that numerical solutions converge to the theoretical solution of the model. The convergence result of numerical solutions of jump-diffusion CKLS model under Markovian switching is applied to a bond pricing problem and the expected return problem of a barrier option. Based on empirical analysis of 7-day Shibor interest rate, jump-diffusion CKLS model under Markovian switching is more valid and effective for modeling dynamic interest rate in China＇s financial market.

关 键 词：马氏转移跳扩散CKLS模型 全局正解 有界性 数值解的收敛性 金融应用 

分 类 号：O211.63[理学—概率论与数理统计]