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

  • Hördahl, Peter

    ()

    (Directorate Monetary Policy)

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
Date of revision:
Handle: RePEc:hhs:rbnkwp:0111
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  1. 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.
  2. Broze, L. & Scaillet, O. & Zakoïan, J.-M., . "Testing for continuous-time models of the short-term interest rate," CORE Discussion Papers RP -1177, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  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 1209-27, July.
  4. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
  5. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  6. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  7. Paul Soderlind & Lars E. O. Svensson, 1997. "New Techniques to Extract Market Expectations from Financial Instruments," NBER Working Papers 5877, National Bureau of Economic Research, Inc.
  8. 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.
  9. 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.
  10. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May.
  11. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, . "Evaluating Density Forecasts," CARESS Working Papres 97-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  12. 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 163-83, June.
  13. 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.
  14. Bhupinder Bahra, 1997. "Implied risk-neutral probability density functions from option prices: theory and application," Bank of England working papers 66, Bank of England.
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