Empirical Analyses of Dynamic
Term Structure Models
WE TURN NEXT to the estimation and assessments of fit of DTSMs. Focusing primarily on the parametric models just surveyed and drawing upon Chapter 5, we begin by reviewing alternative estimation strategies. The goodnessof-fit of DTSMs is then explored in two steps. First, we describe several notable empirical features of the historical behavior of bond yields that have been widely viewed as “puzzles.” We present these as challenges that a successful DTSM should resolve, roughly speaking, by producing a match between certain moments of the model-implied and historical conditional distributions of bond yields.
Chapter 5 introduced several estimation strategies for continuous-time models. Most of these methods are applicable to DTSMs, after making the requisite modifications to accommodate the fact that the state vector Y is observed only indirectly through the DTSM. We begin our discussion of estimation with affine models.
Let ψ0 denote the population parameters governing an affine DTSM and suppose that zero-coupon bond prices are to be used in estimation. If we let yt denote an N-dimensional vector of yields on these bonds, it follows from (12.7) thatyt = A(ψ0) + B(ψ0)Yt, where Yt follows an affine diffusion, and the N×1 vector A and N×N matrix B are determined by an affine pricing model.1 The parameter vector ψ0 includes the parameters governing
1 Recalling that the yield on a zero-coupon bond is defined as –logD(t, T)/τ, τ = (T – t), note that the components of A and B are γ0(τ) and γY(τ) from (12.7) scaled by 1/τ.