Linear or Non-Linear: This is the Dilemma!

Estimation of the unknown drift and diffusion terms of a stochastic process representing the spot interest rate has received increased attention in the financial literature. In this brief paper, we analyze the performance of the two most popular non-parametric approaches to the problem, Sahalia’ s FGLS and Stanton’ s Taylor Expansion. An outright estimation of each of the proposed models to a sample of 22 years of daily observations of the 7-days eurodollar spot interest rate seems to suggest the existence of non-linearity in both the reversion and the volatility of the rate process. However, the results of a series of simulations from a known process reveal that none of the methods here examined has enough power to recognize a “true” linear drift, i.e. that the linearity of the interest rate drift component is rejected “too often”. More accuracy is however found for the estimated diffusion. We are then inclined to confirm Sahalia’ s claim that the volatility of the spot rate appears to be increasing with the level of the rate. * Ph.D. candidate at the Stern School of Business. Please address comments to the author at the Leonard N. Stern School of Business, New York University, Kaufman Management Education Center, Suite 9-190, 44 West 4th Street, New York, NY 10012-1126, or through email: [email protected]. 1