European Vanilla Option Pricing Model of Fractional Order without Singular Kernel

By Mehmet Yavuz, Necati Özdemir. 2018

115 citations recorded by the source corpus.

Recently, fractional differential equations (FDEs) have attracted much more attention in modeling real-life problems. Since most FDEs do not have exact solutions, numerical solution methods are used commonly. Therefore, in this study, we have demonstrated a novel approximate-analytical solution method, which is called the Laplace homotopy analysis method (LHAM) using the Caputo–Fabrizio (CF) fractional derivative operator. The recommended method is obtained by combining Laplace transform (LT) and the homotopy analysis method (HAM). We have used the fractional operator suggested by Caputo and Fabrizio in 2015 based on the exponential kernel. We have considered the LHAM with this derivative in order to obtain the solutions of the fractional Black–Scholes equations (FBSEs) with the initial conditions. In addition to this, the convergence and stability analysis of the model have been constructed. According to the results of this study, it can be concluded that the LHAM in the sense of the CF fractional derivative is an effective and accurate method, which is computable in the series easily in a short time.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/26cb85682364f6f629a06ea3283209bac8457a35

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In Applied Mathematics

1. Mehmet Yavuz
2. Ndolane Sene
3. Necati Özdemir
4. Hasan Bulut

In Modeling and Simulation

1. Mehmet Yavuz
2. Ndolane Sene
3. Necati Özdemir
4. Tukur Abdulkadir Sulaiman
5. Fuat Usta
6. Hasan Bulut

In Numerical Analysis

1. Mehmet Yavuz
2. Ndolane Sene
3. Necati Özdemir
4. Tukur Abdulkadir Sulaiman
5. Hasan Bulut

Citations in the corpus

• Analysis and numerical computations of the fractional regularized long‐wave equation with damping term (2020, background): “Taking the norm of both sides of Equation (23), we get”
• Comparing the new fractional derivative operators involving exponential and Mittag-Leffler kernel (2020, background): “Some interesting studies such as [17, 10, 2, 3, 18, 25, 24, 8] have been resulted in the sense of the CFO.”
• Stability Analysis and Numerical Computation of the Fractional Predator–Prey Model with the Harvesting Rate (2020, background): “Because of effective properties, fractional order calculus has found wide applications to model dynamics processes in many well-known fields, such as biology [6–11], physics [12–16], finance and economics [17,18], science and engineering [19,20], mechanics and mathematical modeling [21,22].”
• Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag–Leffler kernel differential operator (2021, unknown): “Next, CR T ×R×R ð Þ denotes the set of all continuous crisp functions on T ×R×R: Hither, we assume the following subordinate: xn−1 1⁄2 Tr  is bounded as n ! ∞, ti f gi=1 is dense on T , and the solution of Equation (24) is unique and exists in  T ð Þ: Now, we will show the convergence of x t ð Þ 1”