A Hybrid Spectral-Finite Difference Method for Numerical Pricing of Time-Fractional Black–Scholes Equation

Nasibeh Mollahasani ()
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Nasibeh Mollahasani: Graduate University of Advanced Technology

Computational Economics, 2024, vol. 64, issue 2, No 9, 869 pages

Abstract: Abstract In this paper, option pricing through introducing a novel hybrid method for solving time-fractional Black–Scholes equation is considered. The presented method is based on time and space discretization. Time discretization is according to a second order finite difference formula. Space discretization is done by a spectral method based on fractional order shifted Hahn functions (FOSHFs) and an operational process by defining fractional order Hahn operational matrices. Convergence and error analysis for FOSHFs approximation and also for the proposed method are discussed. For validating obtained theoretical results and demonstrating the accuracy, convergency and efficiency of the method, two numerical examples with the known exact solutions are considerd and compared to other methods. Furthermore, the presented method is used to price three different European options governed by a time-fractional Black–Scholes model: European call option, European put option and European double barrier knock-out call option.

Keywords: Numerical pricing; Fractional Black–Scholes equation; Hybrid spectral method; Error analysis; Fractional Hahn functions; 65M70; 65M22; 65M15; 35R11; 26A33 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10614-023-10441-z

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