A Stable and Convergent Finite Difference Method for Fractional Black–Scholes Model of American Put Option Pricing

R. Kalantari () and S. Shahmorad ()
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R. Kalantari: University of Tabriz
S. Shahmorad: University of Tabriz

Computational Economics, 2019, vol. 53, issue 1, No 9, 205 pages

Abstract: Abstract We introduce the mathematical modeling of American put option under the fractional Black–Scholes model, which leads to a free boundary problem. Then the free boundary (optimal exercise boundary) that is unknown, is found by the quasi-stationary method that cause American put option problem to be solvable. In continuation we use a finite difference method for derivatives with respect to stock price, Grünwal Letnikov approximation for derivatives with respect to time and reach a fractional finite difference problem. We show that the set up fractional finite difference problem is stable and convergent. We also show that the numerical results satisfy the physical conditions of American put option pricing under the FBS model.

Keywords: Fractional differential equation; American option pricing; Quasi-stationary; Finite difference method; Newton interpolation method (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10614-017-9734-0

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