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Arbitrage Opportunities in Arbitrage-Free Models of Bond Pricing

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  • David Backus
  • Silverio Foresi
  • Stanley Zin

Abstract

Mathematical models of bond pricing are used by both academics and Wall Street practitioners, with practitioners introducing time-dependent parameters to fit arbitrage-free models to selected asset prices. We show, in a simple one-factor setting, that the ability of such models to reproduce a subset of security prices need not extend to state-contingent claims more generally. The popular Black-Derman-Toy model, for example, overprices call options on long bonds relative to those on short bonds when interest rates exhibit mean reversion. We argue, more generally, that the additional parameters of arbitrage-free models should be complemented by close attention to fundamentals, which might include mean reversion, multiple factors, stochastic volatility, and/or non-normal interest rate distributions.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 5638.

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Date of creation: Jun 1996
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Publication status: published as Backus, David, Silverio Foresi and Stanley Zin. "Arbitrage Opportunities In Arbitrage-Free Models On Bond Pricing," Journal of Business and Economic Statistics, 1998, v16(1,Jan), 13-26.
Handle: RePEc:nbr:nberwo:5638

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  1. 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.
  2. 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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  5. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
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  7. Cooley, T.F. & LeRoy, S.F., 1991. "Pricing Interest-Sensitive Claims when Interest Rates Have Stationary Components," Papers 91-02, Rochester, Business - General.
  8. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn.
  9. 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.
  10. 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.
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Cited by:
  1. Jonathan B. Berk & Richard C. Green & Vasant Naik, 1999. "Optimal Investment, Growth Options, and Security Returns," Journal of Finance, American Finance Association, vol. 54(5), pages 1553-1607, October.
  2. Jin-Chuan Duan & Kris Jacobs, 2001. "Short and Long Memory in Equilibrium Interest Rate Dynamics," CIRANO Working Papers 2001s-22, CIRANO.
  3. David K. Backus & Silverio Foresi & Chris Telmer, . "Discrete time models of bond pricing," GSIA Working Papers 251, Carnegie Mellon University, Tepper School of Business.
  4. Orazio Di Miscia, 2005. "Estimation of continuous-time interest rate models: a nonparametric approach," Finance 0504015, EconWPA.
  5. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
  6. Teresa Corzo Santamaría & Javier Gómez Biscarri, 2005. "Nonparametric estimation of convergence of interest rates: Effects on bond pricing," Spanish Economic Review, Springer, vol. 7(3), pages 167-190, 09.
  7. Orazio Di Miscia, 2005. "Term structure of interest models: concept and estimation problem in a continuous-time setting," Finance 0504017, EconWPA.
  8. Adam Golinski & Peter Spencer, 2012. "The Meiselman forward interest rate revision regression as an Affine Term Structure Model," Discussion Papers 12/27, Department of Economics, University of York.
  9. Dennis Kristensen, 2004. "A Semiparametric Single-Factor Model of the Term Structure," FMG Discussion Papers dp501, Financial Markets Group.
  10. Eli M. Remolona & Joseph Dziwura & Irene Pedraza, 1995. "The short end of the forward convergence curve and asymmetric cat's tail convergence," Research Paper 9523, Federal Reserve Bank of New York.
  11. Xibin Zhang & Robert D. Brooks & Maxwell L. King, 2007. "A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation," Monash Econometrics and Business Statistics Working Papers 11/07, Monash University, Department of Econometrics and Business Statistics.
  12. Leo Krippner, 2005. "An Intertemporally-Consistent and Arbitrage-Free Version of the Nelson and Siegel Class of Yield Curve Models," Working Papers in Economics 05/01, University of Waikato, Department of Economics.
  13. Longstaff, Francis A. & Santa-Clara, Pedro & Schwartz, Eduardo S., 2001. "Throwing away a billion dollars: the cost of suboptimal exercise strategies in the swaptions market," Journal of Financial Economics, Elsevier, vol. 62(1), pages 39-66, October.
  14. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
  15. Michael W. Brandt & Amir Yaron, 2003. "Time-Consistent No-Arbitrage Models of the Term Structure," NBER Working Papers 9458, National Bureau of Economic Research, Inc.

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