Haar wavelet transform and variational iteration method for fractional option pricing models

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.

Review of the Fractional Black-Scholes Equations and Their Solution Techniques

“…Meng et al [113] considered the numerical approximation of the same equation presented in [43] using a combined approach involving the Haar wavelet integration method, the variational iteration method (VIM), and the HPM. The HPM and VIM are widely recognized as efficient tools for solving nonlinear problems.…”

A New X-ray Medical-Image-Enhancement Method Based on Multiscale Shannon–Cosine Wavelet

“…Therefore, ensuring that improvements on image problems are parallel is of great significance for many image-processing applications. In contrast, the wavelet transform has the advantages of easy noise removal, ease of operation, and the ability to reflect information on image feature points [ 14 , 15 , 16 ]. In this work, in order to achieve a dynamic capture and an accurate representation of dynamic curve features, we first use the fluctuation and continuity of the Shannon wavelet function to design a parametric window function according to the integral median theorem, and then through parameter adjustment, we can meet the requirements for the adaptive control of the Shannon–Cosine wavelet on the support interval and smoothness, so as to achieve the texture of medical images The result is a parametric window function that can be adapted to meet the requirements of the Shannon–Cosine wavelet on the support interval and smoothness, to achieve texture approximation in medical images.…”