Term Structure Models

Bond yields and forward rates are defined. The fundamental PDE is derived. Affine term strucure models are explained, including the Vasicek model and the Cox‐Ingersoll‐Ross square root model. Gaussian affine models, completely affine models, and multifactor CIR models are explained. Quadratic models are described. The various versions of the expectations hypothesis are explained. We can fit a given yield curve by adding a deterministic function of time to an interest rate model or allowing model parameters to be time varying. Heath‐Jarrow‐Morton models are explained, and it is shown that drifts of forward rates under the risk neutral probability are determined by their volatilities.