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Reverse Engineering the Yield Curve

  • David K. Backus
  • Stanley E. Zin

Prices of riskfree bonds in any arbitrage-free environment are governed by a pricing kernel: given a kernel, we can compute prices of bonds of any maturity we like. We use observed prices of multi-period bonds to estimate, in a log-linear theoretical setting, the pricing kernel that gave rise to them. The high-order dynamics of our estimated kernel help to explain why first-order, one-factor models of the term structure have had difficulty reconciling the shape of the yield curve with the persistence of the short rate. We use the estimated kernel to provide a new perspective on Hansen-Jagannathan bounds, the price of risk, and the pricing of bond options and futures.

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Paper provided by New York University, Leonard N. Stern School of Business, Department of Economics in its series Working Papers with number 94-09.

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Date of creation: 1994
Date of revision:
Handle: RePEc:ste:nystbu:94-09
Contact details of provider: Postal: New York University, Leonard N. Stern School of Business, Department of Economics, 44 West 4th Street, New York, NY 10012-1126
Phone: (212) 998-0860
Fax: (212) 995-4218
Web page: http://w4.stern.nyu.edu/economics/

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  1. Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December.
  2. David K. Backus, 1993. "Long-Memory Inflation Uncertainty: Evidence from the Term Structure of Interest Rates," Working Papers 93-04, New York University, Leonard N. Stern School of Business, Department of Economics.
  3. 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.
  4. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  5. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-52.
  6. John Y. Campbell, 1984. "Bond and Stock Returns in a Simple Exchange Model," NBER Working Papers 1509, National Bureau of Economic Research, Inc.
  7. Meulbroek, Lisa, 1992. " A Comparison of Forward and Futures Prices of an Interest Rate-Sensitive Financial Asset," Journal of Finance, American Finance Association, vol. 47(1), pages 381-96, March.
  8. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  9. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-62, April.
  10. Gibbons, Michael R & Ramaswamy, Krishna, 1993. "A Test of the Cox, Ingersoll, and Ross Model of the Term Structure," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 619-58.
  11. 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.
  12. Turnbull, Stuart M & Milne, Frank, 1991. "A Simple Approach to Interest-Rate Option Pricing," Review of Financial Studies, Society for Financial Studies, vol. 4(1), pages 87-120.
  13. Longstaff, Francis A & Schwartz, Eduardo S, 1992. " Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-82, September.
  14. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-09, March.
  15. Michael J. Brennan and Eduardo S. Schwartz., 1979. "A Continuous-Time Approach to the Pricing of Bonds," Research Program in Finance Working Papers 85, University of California at Berkeley.
  16. John H. Cochrane & Lars Peter Hansen, 1992. "Asset Pricing Explorations for Macroeconomics," NBER Working Papers 4088, National Bureau of Economic Research, Inc.
  17. Geert Bekaert & Robert J. Hodrick, 1991. "Characterizing Predictable Components in Excess Returns on Equity and Foreign Exchange Markets," NBER Working Papers 3790, National Bureau of Economic Research, Inc.
  18. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
  19. Gallant, Ronald & Tauchen, George, 1989. "Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Econometrica, Econometric Society, vol. 57(5), pages 1091-1120, September.
  20. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  21. Sun, Tong-sheng, 1992. "Real and Nominal Interest Rates: A Discrete-Time Model and Its Continuous-Time Limit," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 581-611.
  22. Stambaugh, Robert F., 1988. "The information in forward rates : Implications for models of the term structure," Journal of Financial Economics, Elsevier, vol. 21(1), pages 41-70, May.
  23. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
  24. Schaefer, Stephen M & Schwartz, Eduardo S, 1987. " Time-Dependent Variance and the Pricing of Bond Options," Journal of Finance, American Finance Association, vol. 42(5), pages 1113-28, December.
  25. Brennan, Michael J. & Schwartz, Eduardo S., 1979. "A continuous time approach to the pricing of bonds," Journal of Banking & Finance, Elsevier, vol. 3(2), pages 133-155, July.
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