Haar wavelet transform and variational iteration method for fractional option pricing models. (4th May 2022)

• Record Type: Journal Article
• Authors: Meng, Liu; Kexin, Meng; Ruyi, Xing; Mei, Shuli; Cattani, Carlo
• Other Names: Singh Jagdev guestEditor.; Kumar Devendra guestEditor.; Baleanu Dumitru guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 7(2023)
• Page Start: 8408
• Page End: 8417
• Publication Date: 2022-05-04
• Subjects: fractional differential equation -- nonlinear Black Scholes; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8343
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Comparing with the linear Black–Scholes model, the fractional option pricing models are constructed by taking account some more parameters like, for example, the transaction cost, so that it becomes more difficult to find the exact analytical solution. In this paper, we analyze a nonlinear fractional Black and Scholes model, and we find the solution by using a novel numerical method, based on a mixture of efficient techniques. In particular, we combine (1) Haar wavelet integration method which transforms the PDEs into a system of algebraic equations, (2) the homotopy perturbation method in order to linearize the problem, and (3) the variational iteration method which will be used to solve the large system of algebraic equations efficiently. We will also show that, in comparison with other popular methods, our coupling technique has a higher efficiency and calculation precision.