Estimation of affine term structure models under the Milstein approximation

This article suggests the Milstein approximation in the estimation of affine term structure models by the Kalman filter. By doing so, affine term structure models with various specifications of the market price of risk can be estimated in a tractable and reasonable manner. In regard to both in-sample fit and out-of-sample forecast, the performance of the Milstein approximation is very close to that of the closed form of the conditional moments. Monte Carlo simulation also shows that the properties of estimators under the Milstein approximation are comparable to those using the closed form of the conditional mean and variance. These indicate that the Milstein approximation can be a good alternative when the closed form of the conditional moments is impractical.