A new method for evaluating options based on multiquadric RBF-FD method

Golbabai, A.; Mohebianfar, Ehsan

doi:10.1016/j.amc.2017.03.019

Cited by 13 publications

(5 citation statements)

References 51 publications

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“…RBF-DQ method originated from the concept of differential quadrature (DQ) [33,34], however, it cannot directly be applied to the problems with irregular geometries. Due to the vast flexibility, RBF-DQ method has been successfully used to study many scientific and engineering problems with irregular geometries [22,32,[35][36][37][38][39][40][41]. In this method, the interpolation coefficients are only dependent on the distributions of the points and independent of the solution.…”

Section: Introductionmentioning

confidence: 99%

A novel local Hermite radial basis function‐based differential quadrature method for solving two‐dimensional variable‐order time fractional advection–diffusion equation with Neumann boundary conditions

Liu

2023

Numerical Methods Partial

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A novel Hermite radial basis function-based differential quadrature (H-RBF-DQ) method is presented in this paper based on 2D variable order time fractional advection-diffusion equations with Neumann boundary conditions. The proposed method is designed to treat accurately for derivative boundary conditions, which considerably improve the approximation results and extend the range of applicability for the method of RBF-DQ. The advantage of the present method is that the Hermite interpolation coefficients are only dependent of the point distribution yielding a substantially better imposition of boundary conditions, even for time evolution. The proposed algorithm is thoroughly validated and is demonstrated to handle the fractional calculus problems with both Dirichlet and Neumann boundaries very well.

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Section: Introductionmentioning

confidence: 99%

A novel local Hermite radial basis function‐based differential quadrature method for solving two‐dimensional variable‐order time fractional advection–diffusion equation with Neumann boundary conditions

Liu

2023

Numerical Methods Partial

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“…e most famous PDE in finance is the Black-Scholes (B-S) model, which is broadly adopted for option pricing. So far, studies have presented different approaches for finding the numerical solution of this model and its variation when the exact form does not exist [5][6][7][8][9][10][11][12][13]. By using tick-by-tick data, Cartea and del-Castillo-Negrete [14] found that the value of European-style options satisfies a FPDE containing a nonlocal operator in time-to-maturity known as the Caputo fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Novel ANN Method for Solving Ordinary and Time‐Fractional Black–Scholes Equation

Bajalan

2021

Complexity

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The main aim of this study is to introduce a 2-layered artificial neural network (ANN) for solving the Black–Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed to change the model into a sequence of ordinary differential equations (ODE). Subsequently, each of these ODEs is solved with the aid of an ANN. Adam optimization is employed as the learning paradigm since it can add the foreknowledge of slowing down the process of optimization when getting close to the actual optimum solution. The model also takes advantage of fine-tuning for speeding up the process and domain mapping to confront the infinite domain issue. Finally, the accuracy, speed, and convergence of the method for solving several types of the Black–Scholes model are reported.

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“…Among others, this also holds for the popular Radial Basis Function-generated Finite Differences method (RBF-FD) [12]. Despite the need for quality node distributions, solving PDEs with strong form meshless methods utilizing radial basis functions (RBFs) has become increasingly popular [13], with recent uses in linear elasticity [35], contact problems [36], geosciences [12], fluid mechanics [19], dynamic thermal rating of power lines [21] and even in the financial sector [15].…”

Section: Introductionmentioning

confidence: 99%

“…for j ← 1 to n do 12: p ← uniform random point in annulus with center S[i] and radii h and 2h 13: if not outside(p, obb) and not tooClose(p, h, G, S) then 14: Add(A, size(S)) Add sequential index of p to active set A. 15:…”

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confidence: 99%

On Generation of Node Distributions for Meshless PDE Discretizations

Slak¹,

Kosec²

2019

SIAM J. Sci. Comput.

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In this paper we present an algorithm that is able to generate locally regular node layouts with spatially variable nodal density for interiors of arbitrary domains in two, three and higher dimensions. It is demonstrated that the generated node distributions are suitable to use in the RBF-FD method, which is demonstrated by solving thermo-fluid problem in 2D and 3D. Additionally, local minimal spacing guarantees are proven for both uniform and variable nodal densities. The presented algorithm has time complexity O(N ) to generate N nodes with constant nodal spacing and O(N log N ) to generate variably spaced nodes. Comparison with existing algorithms is performed in terms of node quality, time complexity, execution time and PDE solution accuracy.

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A new method for evaluating options based on multiquadric RBF-FD method

Cited by 13 publications

References 51 publications

A novel local Hermite radial basis function‐based differential quadrature method for solving two‐dimensional variable‐order time fractional advection–diffusion equation with Neumann boundary conditions

A novel local Hermite radial basis function‐based differential quadrature method for solving two‐dimensional variable‐order time fractional advection–diffusion equation with Neumann boundary conditions

Novel ANN Method for Solving Ordinary and Time‐Fractional Black–Scholes Equation

On Generation of Node Distributions for Meshless PDE Discretizations

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