THE BOND MARKETS: Estimation 3

The Pervasiveness of the Non-linear Drift. In recent papers, Ait-Sahalia [2], Conley, Hansen, Luttmer and Scheinkman [20], and Stanton [39] have found the drift of the short rate to be non-linear in the lagged interest rate. This may simply be an outcome of the specification of the stochastic process as a diffusion.

The critical parameters are (a2j аз)- They examine whether the drift is a function of squared interest rates or inversely related to interest rate levels. If any of these parameters is significantly different from zero, it means that the drift term is nonlinear. The results are presented in Table 10.

The ARCH diffusion model failed to converge. It is evident from the table that the introduction of the jump does diminish the size of the non-linear coefficients (<*2,0:3). There is also a reduction in the level of significance. In fact the non-linearity parameters are significant at the 95% level but not at the 99% level once the jump model is introduced. Hence, it is possible that the jumps do make the model linear in drift. However, from the results here, this is not a strong conclusion, though it is suggestive. It is important to note that the introduction of non-linearity in the drift does not eliminate the statistical significance of the jump process. payday loans online same day

We plot in Figure 2 the graph of the drift term for the pure-diffusion model and the jump-diffusion model. The dotted line shows the drift in the pure-diffusion model for interest, rates varying from 1% to 12%. The full line depicts the jump-diffusion model. The non-linearity diminishes with the introduction of jumps in the extreme ranges of the graph.
It is also likely that the jump model with time-varying jump means may resolve the non-linear drift issue. Since it appears that jumps tend to be positively skewed at lower interest rates, and negatively skewed at high rates (see Table 4), explicitly accounting for this fact may result in the drift becoming linear in the short rate.