An econometric analysis of continuous-time models of the term structure of interest rates is presented. A panel of coupon bond prices with different maturities is used to estimate the embedded parameters of a continuous-discrete state space model of unobserved state variables: the spot interest rate, the central tendency and stochastic volatility. Emphasis is placed on the particular class of exponential-affine term structure models that permits solving the bond pricing PDE in terms of a system of ODEs. It is assumed that coupon bond prices are contaminated by additive white noise, where the stochastic noise term should account for model errors. A nonlinear filtering method is used to compute estimates of the state variables, and the model parameters are estimated by a quasi-maximum likelihood method provided that some assumptions are imposed on the model residuals. Both Monte Carlo simulation results and empirical results based on the Danish bond market are presented.
Nonlinear filtering, quasi maximum likelihood estimation, state space models, stochastic differential equations, stochastic volatility, term structure modelling