Estimating the implied distribution of the future short term interest rate using the Longstaff-Schwartz model

Abstract

This paper proposes the use of the two-factor term-structure model of Longstaff and Schwartz (1992a, LS) to estimate the risk-neutral density (RND) of the future short-term interest rate. The resulting RND can be interpreted as the market's estimate of the density of the future short-term interest rate. As such, it provides a useful financial indicator of the perceived uncertainty of future developments in the short-term interest rate. The LS approach used in this paper provides an alternative to option-based estimation procedures, which may be useful in situations here options markets are not sufficiently developed to allow estimation of the implied distribution from observed option prices. A simulation-based comparison of these two approaches reveals that the differences in the results are relatively small in magnitude, at least for short forecast horizons. Furthermore, the LS model is quite successful in capturing the asymmetries of the true distribution. It is therefore concluded that the LS model can be useful for estimating the distribution of future interest rates, when the purpose is to provide a general measure of the market' s perceived uncertainty, for example as an indictor for monetary policy purposes. JEL Classification: C15, E43, E47, G12