Estimating Affine Term Structure Models from the Cross-Section of Swap Yields

Abstract

It is well known that for affine term structure models, many existing estimates of the parameters characterizing the price of risk and the time series properties of the factors are biased. We argue that this bias can be remedied by using contracts that are non-linear in the state variables in estimation, and we illustrate this by estimating on the cross section of swap yields. While it is recognized that estimation using the raw swap rates is preferable, this is not done in the literature because it is thought to be computationally demanding. Existing studies either convert these swap yields to zero-coupon yields, which linearizes the relationship between the state variables and the observed yields, or they linearize the relationship between the data and the state variables in some other way. We propose the use of the unscented Kalman filter for the estimation of these models on the raw swap data. Our estimates of the price of risk and factor mean reversion differ from estimates obtained using a benchmark method, and an extensive Monte Carlo experiment demonstrates that the unscented Kalman filter leads to important reductions in bias. As a result, our approach yields substantial improvements in out-of-sample forecasts. Our findings suggest that the unscented Kalman filter may prove to be a good approach for a number of problems in fixed income pricing in which the relationship between the state vector and the observations is nonlinear, such as the estimation of term structure models using interest rate derivatives or coupon bonds, and the estimation of quadratic term structure models.