一类多因子利率模型及其性质

A multi-factor interest rate model and its properties

利率在资产定价和风险管理中是一个非常重要的变量。为研究复杂的利率期限结构,提出一个波动率满足Ait-Sahalia模型的高度非线性随机利率模型,并对该模型非负解的存在唯一性、矩有界性以及Euler-Maruyama数值解的收敛性进行证明。采用MATLAB软件对此模型进行数值模拟,验证了这一模型在利率上的适用性。

The interest rate is a very important variable in the asset pricing and risk management.To study the complex term structure of interest rate,a highly nonlinear stochastic interest rate model whose volatility met the Ait-Sahalia model was proposed.Then the existence uniqueness,moment boundedness,and convergence of the non-negative solution of the model and the Euler-Maruyama numerical solution were proved.The applicability of the model to interest rate was verified by numerical simulation using MATLAB software.