Is the Short Rate Drift Actually Nonlinear?

Regime Shifts in a Dynamic Term Structure Model of U.S. Treasury Bond Yields

“…On the other hand, during more "normal" times, variation in the excess returns appears larger in the 1 Ang and Bekaert [2002b] suggest that the mixing of regime-dependent state processes inherent in our DTSM can potentially replicate the nonlinear conditional means of short-term yields documented by AitSahalia [1996] and Stanton [1997]. While the non-parametric evidence for non-linearity in the short-rate process is somewhat controversial (see, e.g., Chapman and Pearson [2000]), the findings of Ang and Bekaert for a Gaussian autoregressive model of a short rate suggest that our regime-dependent state process introduces the flexibility to match such nonlinearity if it is present.…”

Affine Term Structure Models

“…The pattern may, however, be due to small sample biases. Chapman and Pearson (2000) argue that empirical evidence about what happens in the tails of the distribution, far away from the mean, is necessarily based on few data points. Moreover, they simulate short-rate data under the null of an affine conditional mean and find nonlinearities in the mean using the nonparametric estimators of Aït-Sahalia (1996) and Stanton (1997).…”

A Multifactor, Nonlinear, Continuous‐Time Model of Interest Rate Volatility*

“…One way to interpret this result is in the context of the existing literature which shows how di cult it is to estimate low fequency phenomena, like mean reversion, in interest rates see, for example, Bandi 1998 , Chapman and Pearson 1998, Jones 1998and Pritzker 1998 . While the reliability of the estimates in Figure 3 are, therefore, in question, it is interesting to note that the shape of the curve falls in line with standard intuition.…”

“…In a nonparametric framework, Ait-Sahalia 1996a,b develops a procedure for estimating the underlying process for interest rates using discrete data by c hoosing a model for the drift of interest rates and then nonparametrically estimating its di usion function. As an alternative method, Stanton 1997 employs approximations to the true drift and di usion of the underlying process, and then nonparametrically estimates these approximation terms to back out the continuous-time process see also Bandi 1998, Chapman and Pearson 1998and Pritzker 1998 . The advantage of this approach is twofold: i similar to the other procedures, the data need only be observed at discrete time intervals, and ii the drift and di usion are unspeci ed, and thus may be highly nonlinear in the state variable.…”