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Lattice Models for Pricing American Interest Rate Claims

Author

Listed:
  • Li, Anlong
  • Ritchken, Peter
  • Sankarasubramanian, L

Abstract

This article establishes efficient lattice algorithms for pricing American interest-sensitive claims in the Heath, Jarrow, and Morton paradigm under the assumption that the volatility structure of forward rates is restricted to a class that permits a Markovian representation of the term structure. The class of volatilities that permits this representation is quite large and imposes no severe restrictions on the structure for the spot rate volatility. The algorithm exploits the Markovian property of the term structure and permits the efficient computation of all types of interest rate claims. Specific examples are provided. Copyright 1995 by American Finance Association.

Suggested Citation

  • Li, Anlong & Ritchken, Peter & Sankarasubramanian, L, 1995. " Lattice Models for Pricing American Interest Rate Claims," Journal of Finance, American Finance Association, vol. 50(2), pages 719-737, June.
  • Handle: RePEc:bla:jfinan:v:50:y:1995:i:2:p:719-37
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    Cited by:

    1. Beliaeva, Natalia & Nawalkha, Sanjay, 2012. "Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models," Journal of Banking & Finance, Elsevier, vol. 36(1), pages 151-163.
    2. Baaquie, Belal E. & Liang, Cui, 2007. "Pricing American options for interest rate caps and coupon bonds in quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 285-316.
    3. Massimo Costabile & Ivar Massabó & Emilio Russo, 2011. "A binomial approximation for two-state Markovian HJM models," Review of Derivatives Research, Springer, vol. 14(1), pages 37-65, April.
    4. Carl Chiarella & Nadima El-Hassan, 1997. "Evaluation of Derivative Security Prices in the Heath-Jarrow-Morton Framework as Path Integrals Using Fast Fourier Transform Techniques," Working Paper Series 72, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    5. Moraleda, Juan M. & Vorst, Ton C. F., 1997. "Pricing American interest rate claims with humped volatility models," Journal of Banking & Finance, Elsevier, vol. 21(8), pages 1131-1157, August.
    6. Fabio Mercurio & Juan M. Moraleda, 1996. "A Family of Humped Volatility Structures," Tinbergen Institute Discussion Papers 96-169/2, Tinbergen Institute.
    7. P. Forsyth & K. Vetzal & R. Zvan, 2002. "Convergence of numerical methods for valuing path-dependent options using interpolation," Review of Derivatives Research, Springer, vol. 5(3), pages 273-314, October.
    8. Thomas Busch & Bent Jesper Christensen & Morten Ørregaard Nielsen, 2006. "The Information Content of Treasury Bond Options Concerning Future Volatility and Price Jumps," Working Papers 1188, Queen's University, Department of Economics.
    9. Peter Ritchken & Iyuan Chuang, 2000. "Interest rate option pricing with volatility humps," Review of Derivatives Research, Springer, vol. 3(3), pages 237-262, October.
    10. Robert R. Bliss & Peter H. Ritchken, 1995. "Empirical tests of two state-variable HJM models," FRB Atlanta Working Paper 95-13, Federal Reserve Bank of Atlanta.
    11. Chiarella, Carl & Clewlow, Les & Musti, Silvana, 2005. "A volatility decomposition control variate technique for Monte Carlo simulations of Heath Jarrow Morton models," European Journal of Operational Research, Elsevier, vol. 161(2), pages 325-336, March.
    12. Patrick Hagan & Diana Woodward, 1999. "Markov interest rate models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(4), pages 233-260.
    13. 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.
    14. Fabio Mercurio & Juan Moraleda, 2001. "A family of humped volatility models," The European Journal of Finance, Taylor & Francis Journals, vol. 7(2), pages 93-116.
    15. Das, Sanjiv Ranjan, 1998. "A direct discrete-time approach to Poisson-Gaussian bond option pricing in the Heath-Jarrow-Morton model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(3), pages 333-369, November.
    16. Massimo Costabile & Ivar Massabó & Emilio Russo, 2013. "A Path-Independent Humped Volatility Model for Option Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(3), pages 191-210, July.
    17. Marat Kramin & Saikat Nandi & Alexander Shulman, 2008. "A multi-factor Markovian HJM model for pricing American interest rate derivatives," Review of Quantitative Finance and Accounting, Springer, vol. 31(4), pages 359-378, November.
    18. Carl Chiarella & Nadima El-Hassan, 1999. "Pricing American Interest Rate Options in a Heath-Jarrow-Morton Framework Using Method of Lines," Research Paper Series 12, Quantitative Finance Research Centre, University of Technology, Sydney.
    19. Riccardo Rebonato & Ian Cooper, 1998. "Coupling backward induction with Monte Carlo simulations: a fast Fourier transform (FFT) approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(2), pages 131-141.
    20. Jirô Akahori, 1999. "On the Quasi Gaussian Interest Rate Models," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 6(1), pages 3-6, January.
    21. Peterson, Sandra & Stapleton, Richard C. & Subrahmanyam, Marti G., 2003. "A Multifactor Spot Rate Model for the Pricing of Interest Rate Derivatives," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(04), pages 847-880, December.
    22. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6.
    23. Mark Broadie & Jérôme B. Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
    24. Marat Kramin & Timur Kramin & Stephen Young & Venkat Dharan, 2005. "A Simple Induction Approach and an Efficient Trinomial Lattice for Multi-State Variable Interest Rate Derivatives Models," Review of Quantitative Finance and Accounting, Springer, vol. 24(2), pages 199-226, January.

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