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Robust Numerical Methods for the Singularly Perturbed Black-Scholes Equation

In: Proceedings of the Conference on Applied Mathematics and Scientific Computing

Author

Listed:
  • J J H Miller

    (Trinity College, Department of Mathematics)

  • G I Shishkin

    (Institute for Mathematics & Mechanics, Russian Academy of Science)

Abstract

We discuss a dimensionless formulation of the Black-Scholes equation for the value of a European call option. We observe that, for some values of the parameters, this may be a singularly perturbed problem. We demonstrate numerically that, in such a case, a standard numerical method on a uniform mesh does not produce robust numerical solutions. We then construct a new numerical method, on an appropriately fitted piecewise-uniform mesh, which generates numerical approximations that converge parameter-uniformly in the maximum norm to the exact solution.

Suggested Citation

  • J J H Miller & G I Shishkin, 2005. "Robust Numerical Methods for the Singularly Perturbed Black-Scholes Equation," Springer Books, in: Zlatko Drmač & Miljenko Marušić & Zvonimir Tutek (ed.), Proceedings of the Conference on Applied Mathematics and Scientific Computing, pages 95-105, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4020-3197-7_4
    DOI: 10.1007/1-4020-3197-1_4
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