A MULTILEVEL APPROACH TO SOLVING THE BLACK–SCHOLES EQUATION

Hedley Morris () and Alfonso Limon ()
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Hedley Morris: School of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711, USA
Alfonso Limon: School of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2010, vol. 13, issue 03, 403-414

Abstract: In this manuscript, we develop a multilevel framework for the pricing of a European call option based on multiresolution techniques. In this approach, the Black–Scholes equation is transformed via finite differences into a system of linear equations, where the form of the implicit operator is used to construct coarse grid projectors. The reduction of the computational resource is achieved by truncating small wavelet coefficients. However, because traditional wavelets fail to prevent oscillations from developing in the Greeks, a multilevel approach is used to retain smoothness in Gamma by incorporating derivative information into the multiresolution analysis.

Keywords: Adaptive grids; wavelets; Black–Scholes; asset pricing (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S0219024910005826

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