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Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation

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Author Info
Heath, David
Jarrow, Robert
Morton, Andrew

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Abstract

This paper studies the binomial approximation to the continuous trading term structure model of Heath, Jarrow, and Morton (1987). The discrete time approximation makes the original methodology accessible to a wider audience, and provides a computational procedure necessary for calculating the contingent claim values derived in the continuous time paper. This paper also extends and generalizes Ho and Lee's (1986) model to include multiple random shocks to the forward rate process and to include an analysis of continuous time limits. The generalization provides insights into the limitations of the existing empirical implementation of Ho and Lee's model.

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Publisher Info
Article provided by Cambridge University Press in its journal Journal of Financial and Quantitative Analysis.

Volume (Year): 25 (1990)
Issue (Month): 04 (December)
Pages: 419-440
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Handle: RePEc:cup:jfinqa:v:25:y:1990:i:04:p:419-440_00

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  1. Juan M. Moraleda & Ton Vorst, 1996. "The Valuation of Interest Rate Derivatives: Empirical Evidence from the Spanish Market," Tinbergen Institute Discussion Papers 96-170/2, Tinbergen Institute. [Downloadable!]
  2. Anurag Gupta & Marti G. Subrahmanyam, 1999. "An Empirical Examination of the Convexity Bias in the Pricing of Interest Rate Swaps," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-001, New York University, Leonard N. Stern School of Business-. [Downloadable!]
    Other versions:
  3. Peter Ritchken & L. Sankarasubramanian, 1992. "On Markovian representations of the term structure," Working Paper 9214, Federal Reserve Bank of Cleveland. [Downloadable!]
  4. Driessen, J. & Klaassen, P. & Melenberg, B., 2000. "The performance of multi-factor term structure models for pricing and hedging caps and swaptions," Discussion Paper 93, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  5. Patrick S. Hagan, Diana E. Woodward, 1999. "Markov interest rate models," Applied Mathematical Finance, Taylor and Francis Journals, vol. 6(4), pages 233-260, December. [Downloadable!] (restricted)
  6. Phelim P. Boyle & Ken Seng Tan & Weidong Tian, 2001. "Calibrating the Black-Derman-Toy model: some theoretical results," Applied Mathematical Finance, Taylor and Francis Journals, vol. 8(1), pages 27-48, March. [Downloadable!] (restricted)
  7. Emmanuelle Clement & Christian Gourieroux & Alain Monfort, 1995. "Linear Factor Models and the Term Structure of Interest Rates," Annales d'Economie et de Statistique, ADRES, issue 40, pages 05, Octobre-D. [Downloadable!]
  8. Sanjiv Ranjan Das, 1997. "An Efficient Generalized Discrete-Time Approach to Poisson-Gaussian Bond Option Pricing in the Heath-Jarrow-Morton Model," NBER Technical Working Papers 0212, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  9. Sanjiv R. Das, 1998. "Poisson-Guassian Processes and the Bond Markets," NBER Working Papers 6631, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  10. Musiela, Marek & Marek Rutkowski, 1996. "Continuous-Time Term Structure Models," Discussion Paper Serie B 377, University of Bonn, Germany. [Downloadable!]
  11. Klaassen, Pieter, 1997. "Solving stochastic programming models for asset/liability management using iterative disaggregation," Serie Research Memoranda 0010, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics. [Downloadable!]
  12. Alexei Onatski & Slava Kargin, 2004. "Dynamics of Interest Rate Curve by Functional Auto-regression," Econometric Society 2004 North American Summer Meetings 229, Econometric Society. [Downloadable!]
    Other versions:
  13. Robert R. Bliss & Peter Ritchken, 1995. "Empirical tests of two state-variable HJM models," Working Paper 95-13, Federal Reserve Bank of Atlanta. [Downloadable!]
  14. Klaassen, Pieter, 1997. "Discretized reality and spurious profits in stochastic programming models for asset/liability management," Serie Research Memoranda 0011, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics. [Downloadable!]
  15. Driessen, J. & Melenberg, B. & Nijman, T., 2000. "Common factors in international bond returns," Discussion Paper 91, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  16. Robert R. Bliss & Ehud I. Ronn, 1997. "Callable U.S. Treasury bonds: optimal calls, anomalies, and implied volatilities," Working Paper 97-1, Federal Reserve Bank of Atlanta. [Downloadable!]
  17. Sanjiv Ranjan Das & Rangarajan K. Sundaram, 1998. "A Direct Approach to Arbitrage-Free Pricing of Derivatives," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-013, New York University, Leonard N. Stern School of Business-. [Downloadable!]
  18. Jirô Akahori & Hiroki Aoki & Yoshihiko Nagata, 2006. "Generalizations of Ho–Lee’s binomial interest rate model I: from one- to multi-factor," Asia-Pacific Financial Markets, Springer, vol. 13(2), pages 151-179, June. [Downloadable!] (restricted)
    Other versions:
  19. Acharya, Viral V & Das, Sanjiv Ranjan & Sundaram, Rangarajan K, 2002. "Pricing Credit Derivatives with Rating Transitions," CEPR Discussion Papers 3329, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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