A hybrid Chelyshkov wavelet-finite differences method for time-fractional black-Scholes equation

Document Type : Research Paper

Authors

1 Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

2 Department of Basic Sciences, School of Mathematical Sciences, P.O. Box 19395-3697, Payame Noor University (PNU), Tehran, Iran

3 Department of Mathematics, Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan, Iran

Abstract

In this paper, a hybrid method for solving time-fractional Black-Scholes equation is introduced for option pricing. The presented method is based on time and space discretization. A second order finite difference formula is used to time discretization and space discretization is done by a spectral method based on Chelyshkov wavelets and an operational process by defining Chelyshkov wavelets operational matrices. Convergence and error analysis for Chelyshkov wavelets approximation and also for the proposed method are discussed. The method is validated and its accuracy, convergency and efficiency are demonstrated through some cases with given accurate solutions. The method is also utilize for pricing various European options conducted by a time-fractional Black-Scholes model

Keywords

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References

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History

  • Receive Date: 19 October 2023
  • Revise Date: 26 April 2024
  • Accept Date: 14 June 2024

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