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

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Author Info
Peter Hördahl () (European Central Bank, Kaiserstrasse 29, Postfach 16 03 19, 60066 Frankfurt am Main, Germany.)
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.

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Paper provided by European Central Bank in its series Working Paper Series with number 16.

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Length: 47 pages
Date of creation: Mar 2000
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Handle: RePEc:ecb:ecbwps:20000016

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Related research
Keywords: Implied distribution; risk-neutral density; Longstaff-Schwartz model; density forecast; interest rate expectations; forecast evaluation.;

References listed on IDEAS
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  1. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July. [Downloadable!] (restricted)
  2. Soderlind, Paul & Svensson, Lars, 1997. "New techniques to extract market expectations from financial instruments," Journal of Monetary Economics, Elsevier, vol. 40(2), pages 383-429, October. [Downloadable!] (restricted)
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  3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November. [Downloadable!] (restricted)
  4. Brenner, Robin J. & Harjes, Richard H. & Kroner, Kenneth F., 1996. "Another Look at Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 85-107, March. [Downloadable!]
  5. Broze, Laurence & Scaillet, Olivier & Zakoian, Jean-Michel, 1995. "Testing for continuous-time models of the short-term interest rate," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 199-223, September. [Downloadable!] (restricted)
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  6. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May. [Downloadable!] (restricted)
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  7. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  8. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  10. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," NBER Technical Working Papers 0215, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  12. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1980. " An Analysis of Variable Rate Loan Contracts," Journal of Finance, American Finance Association, vol. 35(2), pages 389-403, May. [Downloadable!] (restricted)
  13. Dahlquist, Magnus & Svensson, Lars E O, 1996. " Estimating the Term Structure of Interest Rates for Monetary Policy Analysis," Scandinavian Journal of Economics, Blackwell Publishing, vol. 98(2), pages 163-83, June.
  14. Robert Engle & Tim Bollerslev, 1986. "Modelling the persistence of conditional variances," Econometric Reviews, Taylor and Francis Journals, vol. 5(1), pages 1-50. [Downloadable!] (restricted)
  15. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(2), pages 385-426. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Leo Krippner, 2003. "Modelling the Yield Curve with Orthonormalised Laguerre Polynomials: A Consistent Cross-Sectional and Inter-Temporal Approach," Working Papers in Economics 03/02, University of Waikato, Department of Economics. [Downloadable!]
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