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A Multilevel Approach To Solving The Black–Scholes Equation

Author

Listed:
  • 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)

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.

Suggested Citation

  • Hedley Morris & Alfonso Limon, 2010. "A Multilevel Approach To Solving The Black–Scholes Equation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 403-414.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:03:n:s0219024910005826
    DOI: 10.1142/S0219024910005826
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