Parameter estimation of interest rate models

Abstract

The need for mathematical models capable of covering all sorts of interest rate risks, in particular short-term risk, has increased over the past years with the continuous expansion of the fixed-income market. This dissertation shall focus mainly on one-factor short rate models, with particular attention given to the Vasicek model and the Cox-Ingersoll-Ross (CIR) model with reference also to the unrestricted Chan-Karolyi-Longstaff-Sanders (CKLS) Model. These models come in the form of stochastic differential equations (SDEs) where randomness is driven by Brownian Motion process. In order to be able to understand SDEs one requires a deep study of stochastic integration. Thus first we opt to give an overview of the theory of stochastic integration and SDEs which would serve as a good foundation for the rest of the material covered. Next, three well known methods of estimation, the Maximum Likelihood (ML) estimation, the Generalized Method of Moments (GMM) and the Approximate Maximum Likelihood (AML) estimation using Hermite Polynomials are studied and compared. In order to gain an insight of the performance of these estimation techniques, a number of different paths from specified SDEs are simulated and the sensitivity of such estimation methods to different parameters, is studied. Finally the estimation techniques studied are applied to interest rate data provided by the Central Bank of Malta.