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On the enhanced convergence of standard lattice methods for option pricing

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  • Martin Widdicks
  • Ari D. Andricopoulos
  • David P. Newton
  • Peter W. Duck

Abstract

For derivative securities that must be valued by numerical techniques, the trade‐off between accuracy and computation time can be a severe limitation. For standard lattice methods, improvements are achievable by modifying the underlying structure of these lattices; however, convergence usually remains non‐monotonic. In an alternative approach of general application, it is shown how to use standard methods, such as Cox, Ross, and Rubinstein (CRR), trinomial trees, or finite differences, to produce uniformly converging numerical results suitable for straightforward extrapolation. The concept of Λ, a normalized distance between the strike price and the node above, is introduced, which has wide ranging significance. Accuracy is improved enormously with computation times reduced, often by orders of magnitude. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:315–338, 2002

Suggested Citation

  • Martin Widdicks & Ari D. Andricopoulos & David P. Newton & Peter W. Duck, 2002. "On the enhanced convergence of standard lattice methods for option pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 22(4), pages 315-338, April.
    • Handle: RePEc:wly:jfutmk:v:22:y:2002:i:4:p:315-338
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    Cited by:

    1. San-Lin Chung & Pai-Ta Shih, 2007. "Generalized Cox-Ross-Rubinstein Binomial Models," Management Science, INFORMS, vol. 53(3), pages 508-520, March.
    2. 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.
    3. Mark Joshi, 2009. "Achieving smooth asymptotics for the prices of European options in binomial trees," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 171-176.

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