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A Simple Induction Approach and an Efficient Trinomial Lattice for Multi-State Variable Interest Rate Derivatives Models

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Listed:
  • Marat Kramin
  • Timur Kramin
  • Stephen Young
  • Venkat Dharan

Abstract

This paper presents an alternative approach for interest rate lattice construction in the Ritchken and Sankarasubramanian (1995) framework. The proposed method applies a parsimonious induction technique to represent the distribution of auxiliary state variables and value interest rate derivatives. In contrast to other approaches, this technique requires no numerical interpolations, approximations and iterative procedures for pricing interest rate options using a simple backward induction and, therefore, provides significant computational advantages and flexibility with respect to existing implementations. Also, the proposed trinomial interest rate lattice specification provides for a further reduction in computational costs with additional flexibility. The results of this work can be extended to a class of derivatives pricing models with path dependent state variables and generalized to multi-factor models. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • 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.
    • Handle: RePEc:kap:rqfnac:v:24:y:2005:i:2:p:199-226
    DOI: 10.1007/s11156-005-6337-y
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
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    4. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure1," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72, January.
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    6. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    7. Les Clewlow & Chris Strickland, 1998. "Pricing Interest Rate Exotics in Multi-Factor Gaussian Interest Rate Models," Research Paper Series 2, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Barraquand, Jérôme & Martineau, Didier, 1995. "Numerical Valuation of High Dimensional Multivariate American Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(3), pages 383-405, September.
    9. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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    Cited by:

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    2. I.-Doun Kuo, 2011. "Pricing and hedging volatility smile under multifactor interest rate models," Review of Quantitative Finance and Accounting, Springer, vol. 36(1), pages 83-104, January.
    3. 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.

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