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A universal lattice

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  • Ren-Raw Chen
  • Tyler Yang

Abstract

When valuing derivative contracts with lattice methods, one often needs different lattice structures for different stochastic processes, different parameter values, or even different time intervals to obtain positive probabilities. In view of this stability problem, in this paper, we derive a trinomial lattice structure that can be universally applied to any diffusion process for any set of parameter values at any given time interval. It is particularly useful to the processes that cannot be transformed into constant diffusion. This lattice structure is unique in that it does not require branches to recombine but allows the lattice to freely evolve within the prespecified state space. This is in spirit similar to the implicit finite difference method. We demonstrate that this lattice model is easy to follow and program. The universal lattice is applied to time and state dependent processes that have recently become popular in pricing interest rate derivatives. Numerical examples are provided to demonstrate the mechanism of the model. Copyright Kluwer Academic Publishers 1999

Suggested Citation

  • Ren-Raw Chen & Tyler Yang, 1999. "A universal lattice," Review of Derivatives Research, Springer, vol. 3(2), pages 115-133, May.
    • Handle: RePEc:kap:revdev:v:3:y:1999:i:2:p:115-133
    DOI: 10.1023/A:1009646809675
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    1. 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 1011-1029, December.
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    3. Nelson, Daniel B & Ramaswamy, Krishna, 1990. "Simple Binomial Processes as Diffusion Approximations in Financial Models," The Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 393-430.
    4. 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(2), pages 235-254, June.
    5. Peter Ritchken & Rob Trevor, 1999. "Pricing Options under Generalized GARCH and Stochastic Volatility Processes," Journal of Finance, American Finance Association, vol. 54(1), pages 377-402, February.
    6. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    7. Hull, John & White, Alan, 1990. "Valuing Derivative Securities Using the Explicit Finite Difference Method," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(1), pages 87-100, March.
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    Cited by:

    1. Massimo Costabile & Arturo Leccadito & Ivar Massabó, 2009. "Computationally simple lattice methods for option and bond pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 32(2), pages 161-181, November.
    2. Arturo Leccadito & Pietro Toscano & Radu S. Tunaru, 2012. "Hermite Binomial Trees: A Novel Technique For Derivatives Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-36.
    3. Dasheng Ji & B. Brorsen, 2011. "A recombining lattice option pricing model that relaxes the assumption of lognormality," Review of Derivatives Research, Springer, vol. 14(3), pages 349-367, October.
    4. Tianyang Wang & James Dyer & Warren Hahn, 2015. "A copula-based approach for generating lattices," Review of Derivatives Research, Springer, vol. 18(3), pages 263-289, October.

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