Journal of Computational Finance

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A new improvement scheme for approximation methods of probability density functions

Akihiko Takahashi and Yukihiro Tsuzuki

  • A new scheme for improving an approximation method of a probability density function is developed.
  • The authors achieve the improvement of an approximation, whatever the starting approximate density.

ABSTRACT

This paper develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in the Hilbert space projection theorem. Moreover, we apply Dykstra's cyclic projections algorithm for its implementation. Numerical examples for application to an asymptotic expansion method in option pricing demonstrate the effectiveness of our scheme under the stochastic alpha, beta, rho (SABR) model.

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