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Estimating the Implied Distribution of the Future Short-Term Interest Rate Using the Longstaff-Schwartz Model

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Listed author(s):
  • Hördahl, Peter

    ()

    (Directorate Monetary Policy)

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 futur 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 developements 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 where options markets are not sufficiently developed to allow estimation of the implied distribution from observed option prices. A simulation-based comparison of these two approachs 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 the purpose is to provide a general measure of the market´s perceived uncertainty, for example as an indicator for monetary policy purposes.

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Paper provided by Sveriges Riksbank (Central Bank of Sweden) in its series Working Paper Series with number 111.

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Length: 40 pages
Date of creation: 01 Aug 2000
Handle: RePEc:hhs:rbnkwp:0111
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Sveriges Riksbank, SE-103 37 Stockholm, Sweden

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Keywords: Term structure of interest rates; Monetary policy indicators;

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Find related papers by JEL classification:
  • E50 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - General

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  1. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, "undated". "Evaluating Density Forecasts," CARESS Working Papres 97-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  2. 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.
  3. 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 1209-1227, July.
  4. 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.
  5. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
  6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  7. 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.
  8. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
  9. 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.
  10. Bhupinder Bahra, 1997. "Implied risk-neutral probability density functions from option prices: theory and application," Bank of England working papers 66, Bank of England.
  11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  12. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
  13. 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 637-654, May-June.
  14. Dahlquist, Magnus & Svensson, Lars E O, 1996. " Estimating the Term Structure of Interest Rates for Monetary Policy Analysis," Scandinavian Journal of Economics, Wiley Blackwell, vol. 98(2), pages 163-183, June.
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Cited by:

  1. Vahamaa, Sami, 2005. "Option-implied asymmetries in bond market expectations around monetary policy actions of the ECB," Journal of Economics and Business, Elsevier, vol. 57(1), pages 23-38.
  2. 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.

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