Approximate price of the option under discretization by applying fractional quadratic interpolation

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Mesgarani Hamid; Adl Adele; Esmaeelzade Aghdam Yones

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Journal Paper

Paper Information

Journal: COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS Year:2022 | Volume:10 | Issue:4 Page(s): 1075-1085

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Title

Approximate price of the option under discretization by applying fractional quadratic interpolation

Author(s)

Mesgarani Hamid | Adl Adele | Esmaeelzade Aghdam Yones | Issue Writer Certificate

Keywords

Time fractional Black-Scholes model

Square interpolation

Legendre Polynomials

Collocation method

Abstract

The time-fractional Black-Scholes model (TFBSM) governing European options in which the temporal derivative is focused on the Caputo fractional derivative with 0 < β,≤,1 is considered in this article. Approximating financial options with respect to their hereditary characteristics can be well understood and explained due to its outstanding memory effect current in fractional derivatives. Compelled by the stated cause, It is important to find reasonably accurate and successful numerical methods when approaching fractional differential equations. The simulation model given here is developed in two ways: one, the semi-discrete is produced in the time using a quadratic interpolation with the order of precision τ, 3−, α,in the case of a smooth solution, and subsequently, the unconditional stability and convergence order are investigated. The spatial derivative variables are simulated using the collocation approach based on a Legendre basis for the designed full-discrete scheme. Last, we employ various test problems to demonstrate the suggested design’, s high precision. Moreover, the obtained results are compared to those obtained using other methodologies, demonstrating that the proposed technique is highly accurate and practicable.

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APA: Copy

Mesgarani, Hamid, Adl, Adele, & Esmaeelzade Aghdam, Yones. (2022). Approximate price of the option under discretization by applying fractional quadratic interpolation. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 10(4), 1075-1085. SID. https://sid.ir/paper/1057212/en

Vancouver: Copy

Mesgarani Hamid, Adl Adele, Esmaeelzade Aghdam Yones. Approximate price of the option under discretization by applying fractional quadratic interpolation. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS[Internet]. 2022;10(4):1075-1085. Available from: https://sid.ir/paper/1057212/en

IEEE: Copy

Hamid Mesgarani, Adele Adl, and Yones Esmaeelzade Aghdam, “Approximate price of the option under discretization by applying fractional quadratic interpolation,” COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, vol. 10, no. 4, pp. 1075–1085, 2022, [Online]. Available: https://sid.ir/paper/1057212/en

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