Academic journal article Review of Business

Elasticity of Variance and Jackknife Estimation of Short-Term Interest Rates

Academic journal article Review of Business

Elasticity of Variance and Jackknife Estimation of Short-Term Interest Rates

Article excerpt

Executive Summary

In this article, we illustrate that the estimation procedure applied in Chan et al. (1992)--hereafter referred to as CKLS (1992)--for estimating short-term interest rate models suffers from significant estimation bias. We show by Monte Carlo simulations that the application of the jackknife estimation of Quenouille (1956) provides substantial bias reduction. We provide empirical distributions for parameter tests depending on the elasticity of conditional variance of changes in the short-term interest rate. Using daily, weekly and monthly observations of the three-month U.S. Treasury bill yield and the federal funds rate, we demonstrate that the estimation results can depend on both the sampling frequency and the proxy that is used for the short-term interest rate.

1. Introduction

Many asset pricing models use one-factor stochastic differential equations--hereafter referred to as SDE--to capture the dynamics of the short-term interest rate. Since different drift and diffusion functions generate significantly different prices for interest rate sensitive assets, the choice of the corresponding specification is of great importance.

In CKLS (1992) the empirical validity of several continuous-time models is analyzed by means of the generalized method of moments--hereafter GMM--estimation of Hansen (1982). We show that this procedure suffers from significant estimation bias that arises from the estimation of autoregressive models. This bias is likely to have a large impact on pricing interest rate sensitive assets. We show, by Monte Carlo simulations, that the jackknife estimation of Quenouille (1956), first suggested by Phillips and Yu (2005) within the framework of maximum likelihood estimation of continuous-time models, achieves substantial bias reduction.

Furthermore, to examine the importance of mean-reversion, we determine empirical distributions of the associated t-statistics under the null hypothesis that the drift function is zero. Our findings indicate that the distributions depend on the elasticity of the conditional variance of changes in the short-term interest rate. In addition, we consider the empirical distribution of the likelihood ratio--hereafter LR--statistics under the corresponding null models. We find that the distributions do not strictly and exclusively depend on the number of restrictions, but also on the given model that is considered.

Using observations of the three-month U.S. Treasury bill yield and the federal funds rate from January 4, 1954 through March 2, 2006, we demonstrate that the estimation results can depend on both the sampling frequency and the proxy that is used for the short-term interest rate. As indicated by the results, the three-month U.S. Treasury bill yields seem to be non-stationary, such that the role of mean-reversion appears to be negligible. As in CKLS (1992), we find that the conditional variance of changes in the three-month U.S. Treasury bill yield is highly sensitive to the yield level, whereas an exact specification of the elasticity seems to be more important for daily observations, since the null models are rejected more often. In contrary to that result, daily observations of the federal funds rate exhibit significant mean-reversion and a lower sensitivity of the conditional variance of changes in the rate level.

The remainder of this work is organized as follows. Section 2 discusses the stochastic properties of several continuous-time models. Section 3 presents an analysis of the estimation procedure. In Section 4, the results of the Monte Carlo experiments are presented. Section 5 reports the corresponding empirical results. Section 6 concludes.

2. Continuous-Time Models of the Short-Term Interest Rate

CKLS (1992) assume that the short-term interest rate follows a continuous-time stochastic process {[R.sub.t] | t[greater than or equal to] 0} which solves a time-homogenous, one-factor, diffusion-type SDE, of the form

[dR. …

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