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Lattice Models for Pricing American Interest Rate Claims

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  • Li, Anlong
  • Ritchken, Peter
  • Sankarasubramanian, L
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    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.

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    Bibliographic Info

    Article provided by American Finance Association in its journal Journal of Finance.

    Volume (Year): 50 (1995)
    Issue (Month): 2 (June)
    Pages: 719-37

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    Handle: RePEc:bla:jfinan:v:50:y:1995:i:2:p:719-37

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    Cited by:
    1. 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.
    2. 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.
    3. Robert R. Bliss & Peter Ritchken, 1995. "Empirical tests of two state-variable HJM models," Working Paper 95-13, Federal Reserve Bank of Atlanta.
    4. Peter Ritchken & Iyuan Chuang, 2000. "Interest rate option pricing with volatility humps," Review of Derivatives Research, Springer, vol. 3(3), pages 237-262, October.
    5. 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.
    6. 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.
    7. 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.
    8. repec:dgr:uvatin:1996169 is not listed on IDEAS
    9. repec:dgr:uvatin:2096170 is not listed on IDEAS
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Jirô Akahori, 1999. "On the Quasi Gaussian Interest Rate Models," Asia-Pacific Financial Markets, Springer, vol. 6(1), pages 3-6, January.
    15. repec:dgr:uvatin:1996170 is not listed on IDEAS
    16. 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.
    17. Patrick Hagan & Diana Woodward, 1999. "Markov interest rate models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(4), pages 233-260.
    18. 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.
    19. 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.
    20. repec:dgr:uvatin:2096169 is not listed on IDEAS
    21. 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.
    22. Mark Broadie & Jérôme B. Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.

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