A Semiparametric Interest Rate Model Based on Reducible Stochastic Differential Equations and Pseudo Maximum Likelihood Estimation

• Activity Number: 521
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Ruijun Bu and Kaddour Hadri*+
• Companies: Queen's University at Belfast and The University of Liverpool
• Keywords: Semi-parametric Models ; Non-parametric Estimation ; Multivariate Interest Rate Models ; Reducible Stochastic Differential Equations ; Maximum Likelihood Estimation ; Time-Varying Copulas

Abstract

We propose a new semiparametric model for interest rate processes based on Reducible Stochastic Differential Equations (RSDEs). The idea of using RSDEs for modelling interest rates was pioneered by Bu et al (2011) who proposed two classes of nonlinear SDEs that are reducible to either Ornstein-Uhlenbeck or Cox, Ingersoll, and Ross (1985) process via parametric transformations. In this paper, we extend Bu et al (2011) by allowing the transformation function to be completely unspecified. In contrast to existing semiparametric models (e.g. Aït-Sahalia 1996, Kristensen 2010) where either the drift or the diffusion must be completely parametric, both of them are semi-parametric in our framework. Their shapes are thus not limited to the imposed parametric structure. An explicit semiparametric functional estimate of the transition density function is derived. We therefore propose to estimate the model by pseudo maximum likelihood. We further extend our model to multivariate case by the copula approach. In our empirical application, we study the goodness of fit of the new model to UK and US short rates and examine their conditional dependence structure in our multivariate framework.