Continuous-time Parameter Estimation of Exponential-Affine Term Structure Models

The exponential-affine term structure model is a class of models in which the yields to maturity are affine functions of some state vector x(t). This model has been first proposed by Duffie and Kan (1994), and subsumes Vasicek, Cox-Ingersol-Ross and other commonly used interest rate models as special cases.
Since the interest rate factors x(t) are not directly observed, unknown parameters in these models need to be estimated on the basis of observing the bond prices of different maturities. Although financial models are commonly formulated in continuous time, all existing parameter estimation techniques discretize the observation equation in time in order to use known statistical or filtering methods. We resolve this incongruity in the present paper by working throughout with the original continuous-time formulation.