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Annual Review of Financial Economics

Volume 9, 2017

Forward-Looking Estimates of Interest-Rate Distributions

Abstract

This article reviews methods for extracting both risk-neutral and physical density forecasts for interest rates. It presents some applications, with particular focus on issues pertaining to forward guidance and the zero lower bound. Several important applied questions in macroeconomics and monetary economics can be very directly addressed using the wealth of information in interest-rate derivative securities.

Keyword(s): density forecasting, interest rates, options, risk premia, zero lower bound
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2017-11-01
2025-06-23
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Literature Cited

  1. Adrian T, Crump RK, Moench E. 2013. Pricing the term structure with linear regressions. J. Financ. Econ. 110:110–38 [Google Scholar]
  2. Aït-Sahalia Y, Duarte J. 2003. Nonparametric option pricing under shape restrictions. J. Econom. 116:9–47 [Google Scholar]
  3. Aït-Sahalia Y, Lo AW. 1998. Nonparameteric estimation of state-price densities implicit in financial asset prices. J. Finance 53:499–547 [Google Scholar]
  4. Andersen AB, Wagener T. 2002. Extracting risk neutral probability densities by fitting implied volatility smiles: some methodological points and an application to the 3M Euribor futures option prices Work. Pap. 198, Eur. Cent. Bank, Frankfurt, Ger. [Google Scholar]
  5. Andersen T, Benzoni L. 2010. Do bonds span volatility risk in the U.S. Treasury market? A specification test for affine term structure models. J. Finance 65:603–53 [Google Scholar]
  6. Black F. 1976. The pricing of commodity contracts. J. Financ. Econ. 3:167–79 [Google Scholar]
  7. Black F. 1995. Interest rates as options. J. Finance 50:1371–76 [Google Scholar]
  8. Bliss RR, Panigirtzoglou N. 2002. Testing the stability of implied probability density functions. J. Bank. Finance 26:381–422 [Google Scholar]
  9. Brace A, Gatarek D, Musiela M. 1997. The market model of interest rate dynamics. Math. Finance 7:127–54 [Google Scholar]
  10. Breeden DT, Litzenberger RH. 1978. Prices of state contingent claims implicit in options prices. J. Bus. 51:621–51 [Google Scholar]
  11. Brigo D, Mercurio F. 2006. Interest Rate Models—Theory and Practice Berlin: Springer [Google Scholar]
  12. Campbell JY, Sunderam A, Viceira LM. 2009. Inflation bets or deflation hedges? The changing risks of nominal bonds NBER Work. Pap. 14701 Cambridge, MA: [Google Scholar]
  13. Carriero A, Clark TE, Marcellino MG. 2014. No arbitrage priors, drifting volatilities and the term structure of interest rates Discuss. Pap. 9848 Cent. Econ. Policy Res Washington, DC: [Google Scholar]
  14. Chun AL. 2011. Expectations, bond yields, and monetary policy. Rev. Financ. Stud. 24:208–47 [Google Scholar]
  15. Cieslak A, Povala P. 2016. Information in the term structure of yield curve volatility. J. Finance 71:1393–436 [Google Scholar]
  16. Clark TE. 2011. Real-time density forecasts from Bayesian vector autoregressions with stochastic volatility. J. Bus. Econ. Stat. 29:327–41 [Google Scholar]
  17. Cochrane JH, Piazzesi M. 2005. Bond risk premia. Am. Econ. Rev. 95:138–60 [Google Scholar]
  18. Collin-Dufresne P, Goldstein RS. 2002. Do bonds span the fixed income markets? Theory and evidence for unspanned stochastic volatility. J. Finance 57:1685–730 [Google Scholar]
  19. Collin-Dufresne P, Goldstein RS, Jones CS. 2009. Can interest rate volatility be extracted from the cross section of bond yields?. J. Financ. Econ. 94:47–66 [Google Scholar]
  20. Diebold FX, Li C. 2006. Forecasting the term structure of government bond yields. J. Econom. 131:309–38 [Google Scholar]
  21. Duffee GR. 2013. Forecasting interest rates. Handbook of Economic Forecasting 2 G Elliott, A Timmermann 385–426 Amsterdam: Elsevier [Google Scholar]
  22. Egorov AV, Hong Y, Li H. 2006. Validating forecasts of the joint probability density of bond yields: Can affine models beat random walk?. J. Econom. 135:255–84 [Google Scholar]
  23. Elliott D, Noss J. 2015. Estimating market expectations of changes in bank rate. Bank Engl. Q. Bull. 55:273–82 [Google Scholar]
  24. Engelberg J, Manski CF, Williams J. 2009. Comparing the point predictions and subjective probability distributions of professional forecasters. J. Bus. Econ. Stat. 27:30–41 [Google Scholar]
  25. Feldman R, Heinecke K, Kocherlakota N, Schulhofer-Wohl S, Tallarini T. 2015. Market-based probabilities: a tool for policymakers Work. Pap., Fed Reserve Bank Minneap. Minneapolis, MN: [Google Scholar]
  26. Filipović D, Larsson M, Trolle AB. 2017. Linear-rational term structure models. J. Finance 72:655–704 [Google Scholar]
  27. Goldys B, Musiela M, Sondermann D. 2000. Lognormality of rates and term structure models. Stoch. Anal. Appl. 18:375–96 [Google Scholar]
  28. Gürkaynak RS, Sack B, Wright JH. 2007. The U.S. Treasury yield curve: 1961 to the present. J. Monet. Econ. 54:2291–304 [Google Scholar]
  29. Hautsch N, Ou Y. 2012. Analyzing interest rate risk: stochastic volatility in the term structure of government bond yields. J. Bank. Finance 36:2988–3007 [Google Scholar]
  30. Hautsch N, Yang F. 2012. Bayesian inference in a stochastic volatility Nelson–Siegel model. Comput. Stat. Data Anal. 56:3774–92 [Google Scholar]
  31. Heath D, Jarrow RA, Morton A. 1992. Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation. Econometrica 60:77–105 [Google Scholar]
  32. Heidari M, Wu L. 2009. A joint framework for consistently pricing interest rates and interest rate derivatives. J. Financ. Quant. Anal. 44:517–50 [Google Scholar]
  33. Hong Y, Li H, Zhao F. 2004. Out-of-sample performance of discrete time spot interest rate models. J. Bus. Econ. Stat. 22:457–73 [Google Scholar]
  34. Hull J, White A. 1990. Pricing interest-rate derivative securities. Rev. Financ. Stud. 3:573–92 [Google Scholar]
  35. Hull J, White A. 2013. LIBOR versus OIS: the derivatives discount dilemma. J. Invest. Manag. 11:14–27 [Google Scholar]
  36. Ivanova V, Gutiérrez JM. 2014. Interest rate forecasts, state price densities and risk premium from Euribor options. J. Bank. Finance 48:210–23 [Google Scholar]
  37. Jacobs K, Karoui L. 2009. Conditional volatility in affine term-structure models: evidence from Treasury and swap markets. J. Financ. Econ. 91:288–318 [Google Scholar]
  38. Jamshidian F. 2007. An exact bond option formula. J. Finance 44:205–9 [Google Scholar]
  39. Jarrow RA. 2009. The term structure of interest rates. Annu. Rev. Financ. Econ. 1:69–96 [Google Scholar]
  40. Jarrow RA. 2014. Forward rate curve smoothing. Annu. Rev. Financ. Econ. 6:443–58 [Google Scholar]
  41. Jarrow RA, Li H, Zhao F. 2007. Interest rate caps ‘smile’ too! But can the LIBOR market models capture the smile?. J. Finance 62:345–82 [Google Scholar]
  42. Kim DH, Orphanides A. 2012. Term structure estimation with survey data on interest rate forecasts. J. Financ. Quant. Anal. 47:241–72 [Google Scholar]
  43. Kim DH, Singleton KJ. 2012. Term structure models and the zero bound: an empirical investigation of Japanese yields. J. Econom. 170:32–49 [Google Scholar]
  44. Kim DH, Wright JH. 2005. An arbitrage-free three-factor term structure model and the recent behavior of long-term yields and distant-horizon forward rates Work. Pap. 2005-33 Finance Econ. Discuss. Ser., Fed. Reserve Board Washington, DC: [Google Scholar]
  45. Kim DH, Wright JH. 2014. Jumps in bond yields at known times Work. Pap. 2014-100 Finance Econ. Discuss. Ser., Fed. Reserve Board Washington, DC: [Google Scholar]
  46. Koopman SJ, Mallee MIP, der Wel MV. 2010. Analyzing the term structure of interest rates using the dynamic Nelson–Siegel model with time-varying parameters. J. Bus. Econ. Stat.329–43 [Google Scholar]
  47. Krippner L. 2014. Zero Lower Bound Term Structure Modeling: A Practitioner's Guide New York: Palgrave Macmillan [Google Scholar]
  48. Li H, Zhao F. 2009. Nonparametric estimation of state-price densities implicit in interest rate cap prices. Rev. Financ. Stud. 22:4335–76 [Google Scholar]
  49. Litterman R, Scheinkman J. 1991. Common factors affecting bond returns. J. Fixed Income 1:54–61 [Google Scholar]
  50. Longstaff FA, Schwartz ES. 1992. Interest rate volatility and the term structure: a two-factor general equilibrium model. J. Finance 48:1259–82 [Google Scholar]
  51. Nelson CR, Siegel AF. 1987. Parsimonious modeling of yield curves. J. Bus. 60:473–89 [Google Scholar]
  52. Rebonato R. 1999. Volatility and Correlation Chichester, UK: Wiley [Google Scholar]
  53. Rebonato R. 2003. Modern Pricing of Interest Rate Derivatives: The LIBOR Market Model and Beyond Princeton, NJ: Princeton Univ. Press [Google Scholar]
  54. Rognlie M. 2016. What lower bound? Monetary policy with negative interest rates Work. Pap., MIT [Google Scholar]
  55. Rosenberg JV, Engle RF. 2002. Empirical pricing kernels. J. Financ. Econ. 64:341–72 [Google Scholar]
  56. Sandmann K, Sondermann D. 1997. A note on the stability of lognormal interest rate models and the pricing of Eurodollar futures. Math. Finance 7:119–25 [Google Scholar]
  57. Shiller RJ, Campbell JY, Schoenholtz KL. 1983. Forward rates and future policy: interpreting the term structure of interest rates. Brookings Pap. Econ. Act. 1:173–217 [Google Scholar]
  58. Shimko D. 1993. Bounds of probability. Risk 6:33–37 [Google Scholar]
  59. Shreve SE. 2004. Stochastic Calculus for Finance II: Continuous-Time Models New York: Springer [Google Scholar]
  60. Svensson LEO. 1994. Estimating and interpreting forward rates: Sweden 1992–4. NBER Work. Pap. 4871 Cambridge, MA: [Google Scholar]
  61. Swanson ET, Williams JC. 2014. Measuring the effect of the zero lower bound on medium- and longer-term interest rates. Am. Econ. Rev. 104:3154–85 [Google Scholar]
  62. Veronesi P. 2010. Fixed Income Securities Hoboken, NJ: Wiley [Google Scholar]
  63. Wright JH. 2016. Options-implied probability density functions for real interest rates. Int. J. Cent. Bank. 12:3129–49 [Google Scholar]
  64. Wu JC, Xia FD. 2016. Measuring the macroeconomic impact of monetary policy at the zero lower bound. J. Money Credit Bank. 48:253–91 [Google Scholar]
/content/journals/10.1146/annurev-financial-110716-032347
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Forward-Looking Estimates of Interest-Rate Distributions
Annual Review of Financial Economics 9, 333 (2017); https://doi.org/10.1146/annurev-financial-110716-032347
/content/journals/10.1146/annurev-financial-110716-032347
/content/journals/10.1146/annurev-financial-110716-032347
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Supplementary Data

  • Supplemental Video: Options-implied probability density functions (PDFs) for 3-month interest rates 1 year hence.

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