Robust Numerical Methods for the Singularly Perturbed Black-Scholes Equation

J J H Miller () and G I Shishkin ()
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J J H Miller: Trinity College, Department of Mathematics
G I Shishkin: Institute for Mathematics & Mechanics, Russian Academy of Science

A chapter in Proceedings of the Conference on Applied Mathematics and Scientific Computing, 2005, pp 95-105 from Springer

Abstract: 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.

Keywords: Black Scholes; singular perturbation; numerical method; robust (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4020-3197-7_4

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DOI: 10.1007/1-4020-3197-1_4

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