The stability and convergence of the numerical computation for the temporal fractional Black–Scholes equation

Hamid Mesgarani, Masod Bakhshandeh, Yones Esmaeelzade

Abstract


In this paper‎, ‎the temporal fractional Black–Scholes model (TFBSM) is discussed in the limited specific domain which the time derivative of this template‎

‎is the Caputo fractional function‎.

‎The value variance of the associated fractal transmission method was applied to forecast TFBSM‎.

‎For solving‎, ‎at first the semi-discrete scheme is obtained by using linear interpolation with a temporally $\tau^{2-\alpha}$ order accuracy‎.

‎Then‎, ‎the full scheme is collected by approximating the spatial derivative terms by helping‎

‎the Chebyshev collocation system focused on the fourth form‎.

‎Finally‎, ‎the unconditional stability and convergence order is evaluated by performing the energy process‎. ‎As an implementation of this method‎, ‎two examples of the‎

‎TFBSM was reported to demonstrate the accuracy of the developed scheme‎.

‎Calculation simulation and comparison show that the suggested strategy is very accurate and effective.


Keywords


Temporal fractional Black–Scholes model‎, Chebyshev polynomials of the fourth kind‎, Linear interpolation‎, Collocation method‎, Unconditional stability‎, Convergence order

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