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Discrete-Time Models of Bond Pricing

  • David Backus
  • Silverio Foresi
  • Chris Telmer

We explore a variety of models and approaches to bond pricing, including those associated with Vasicek, Cox-Ingersoll-Ross, Ho and Lee, and Heath-Jarrow-Morton, as well as models with jumps, multiple factors, and stochastic volatility. We describe each model in a common theoretical framework and explain the reasoning underlying the choice of parameter values. Our framework has continuous state variables but discrete time, which we regard as a convenient middle ground between the stochastic calculus of high theory and the binomial models of classroom fame. In this setting, most of the models we examine are easily implemented on a spreadsheet.

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File URL: http://www.nber.org/papers/w6736.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 6736.

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Date of creation: Sep 1998
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Publication status: published as Jegadeesh, N. and B. Tuckman (eds.) Advanced Fixed Income Valuation Tools. Wiley, 2000.
Handle: RePEc:nbr:nberwo:6736
Note: AP
Contact details of provider: Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.
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Web page: http://www.nber.org
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  1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  2. David Backus & Silverio Foresi & Liuren Wu, 2002. "Accouting for Biases in Black-Scholes," Finance 0207008, EconWPA.
  3. Qiang Dai & Kenneth J. Singleton, 1997. "Specification Analysis of Affine Term Structure Models," NBER Working Papers 6128, National Bureau of Economic Research, Inc.
  4. David K. Backus & Silverio Foresi & Stanley E. Zin, 1994. "Arbitrage Opportunities in Arbitrage-Free Models of Bond Pricing," Working Papers 94-28, New York University, Leonard N. Stern School of Business, Department of Economics.
  5. Duffie, Darrell & Singleton, Kenneth J, 1997. " An Econometric Model of the Term Structure of Interest-Rate Swap Yields," Journal of Finance, American Finance Association, vol. 52(4), pages 1287-1321, September.
  6. 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.
  7. 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.
  8. 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.
  9. Backus, David & Foresi, Silverio & Mozumdar, Abon & Wu, Liuren, 2001. "Predictable changes in yields and forward rates," Journal of Financial Economics, Elsevier, vol. 59(3), pages 281-311, March.
  10. 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.
  11. Pearson, Neil D & Sun, Tong-Sheng, 1994. " Exploiting the Conditional Density in Estimating the Term Structure: An Application to the Cox, Ingersoll, and Ross Model," Journal of Finance, American Finance Association, vol. 49(4), pages 1279-1304, September.
  12. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
  13. 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.
  14. David Backus & Silverio Foresi & Chris Telmer, 1996. "Affine Models of Currency Pricing," NBER Working Papers 5623, National Bureau of Economic Research, Inc.
  15. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
  16. 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.
  17. Pierluigi Balduzzi & Sanjiv Das & Silverio Foresi, 1996. "The Central Tendency: A Second Factor in Bond Yields," New York University, Leonard N. Stern School Finance Department Working Paper Seires 96-12, New York University, Leonard N. Stern School of Business-.
  18. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(02), pages 235-254, June.
  19. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  20. 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.
  21. 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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