Estimating and Testing an Exponential-Affine Term Structure Model by Nonlinear Filtering

In general, the interest rate is not directly observable in the financial market. Short term interest rates are quoted in the money market for maturities up to approximately one year, but longer term interest rates are traded only indirectly through the bond market. In this paper the spot interest rate is described by a bivariate stochastic differential equation state space model that gives rise to an exponential-affine term structure model. We propose a new maximum likelihood method for estimating parameters and interest rates in stochastic differential equations from observed coupon-bearing bond prices. The method utilizes continuous discrete second order nonlinear filtering techniques. As a preliminary analysis the method is applied to a cross-section of time series of Danish government bond prices.