This paper examines the intertemporal behavior of the short-term rate of interest in a mean-reverting model (Vasicek's elastic random walk model). Using the Goldfeld-Quandt switching regressions technique, we show that the mean-reverting model switched regimes three times over the sample period (March 1959 to December 1985) and that two of these switches coincide with the 1979 and 1982 changes in Federal Reserve monetary policy on interest rates. Parameter estimates prove to be unstable over the sample period. There is evidence of slow mean reversion over the entire sample period; yet significant mean-reversion emerges only in the 1979n1982 regime.

The following paper presents a general derivation of the jump process option pricing formula. In particular, a general jump process formula is derived via an analysis of the limiting behavior of the binomial option pricing formula. In deriving the formula, a very simple central limit theorem known as Poisson's Limit Theorem is applied. The simplicity of the analysis allows the establishment of precisely the connections between the specification of the underlying binomial stock return process and the specific form of the corresponding continuous-time jump process formula. Several examples are provided to illustrate these connections.

We estimate and compare a variety of continuous-time models of the short-term riskless rate using the Generalized Method of Moments. We find that the most successful models in capturing the dynamics of the short-term interest rate are those that allow the volatility of interest rate changes to be highly sensitive to the level of the riskless rate. A number of well-known models perform poorly in the comparisons because of their implicit restrictions on term structure volatility. We show that these results have important implications for the use of different term structure models in valuing interest rate contingent claims and in hedging interest rate risk.

We estimate and compare a variety of continuous‐time models of the short‐term riskless rate using the Generalized Method of Moments. We find that the most successful models in capturing the dynamics of the short‐term interest rate are those that allow the volatility of interest rate changes to be highly sensitive to the level of the riskless rate. A number of well‐known models perform poorly in the comparisons because of their implicit restrictions on term structure volatility. We show that these results have important implications for the use of different term structure models in valuing interest rate contingent claims and in hedging interest rate risk.