Radial basis functions with application to finance: American put option under jump diffusion

Golbabai, A.; Ahmadian, Davood; Milev, Mariyan

doi:10.1016/j.mcm.2011.10.014

Cited by 45 publications

(25 citation statements)

References 14 publications

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“…Due to these eye-catching properties, RBFs have found increasingly widespread applications in various fields such as geology, biology, physical and engineering sciences, applied mathematics, computer science, business studies and so on [12][13][14]29]. …”

Section: Outline Of the Rbf Methodsmentioning

confidence: 99%

Hybrid shape parameter strategy for the RBF approximation of vibrating systems

Golbabai

Rabiei

2012

International Journal of Computer Mathematics

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Shape parameters play an important role in radial basis function (RBF) approximations. Therefore, the choice of them is an active field in numerical analysis research. In this paper, first we review the available strategies in the literature for selecting shape parameters. Then, we introduce an alternative approach called hybrid strategy for scaling the RBFs. This strategy is constructed based on the advantages of the older ones and discards their disadvantages. The efficiency of the new strategy is demonstrated by comparing the effects of different strategies on approximating the eigenvalues of ordinary and partial differential equations with different boundary conditions.

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Section: Outline Of the Rbf Methodsmentioning

confidence: 99%

Hybrid shape parameter strategy for the RBF approximation of vibrating systems

Golbabai

Rabiei

2012

International Journal of Computer Mathematics

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“…(1) together with function (18) where r = K = 1. This equation is known as the Fisher equation or logistic equation (20) and admits the exact progressive wave [19] u(…”

Section: Test Problemmentioning

confidence: 99%

“…Therefore, a RBF facilitates the evaluation of the interpolant without using a mesh. In addition to the approximation theory, RBFs are growing in popularity for solving partial differential equations [14,[20][21][22]36,38]. In some of RBFs-based methods, the accuracy of method generally increases for flat RBF.…”

Section: Introductionmentioning

confidence: 99%

Stability and convergence of radial basis function finite difference method for the numerical solution of the reaction–diffusion equations

Golbabai

Nikpour

2015

Applied Mathematics and Computation

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“…Since 1997 in [12] several authors started applying RBF methods to European-style financial problems and later this approach has found a wider use for valuation of options with early-exercise features, see e.g. [3,9]. Authors in [19] presented an improved RBF method that is 20 times faster than an adaptive finite difference method in one and two space dimensions based several numerical experiments only.…”

Section: Introductionmentioning

confidence: 99%

A Local Radial Basis Function Method for High-Dimensional American Option Pricing Problems

Company

Egorova

Jódar

et al. 2018

Mathematical Modelling and Analysis

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In this work, we apply the local Wendland radial basis function (RBF) for solving the time-dependent multi dimensional option pricing nonlinear PDEs. Firstly, cross derivative terms of the PDE are removed with a change of spatial variables based in LDLT factorization of the diffusion matrix. Then, it is discussed that the valuation of a multi-asset option up to 4D can be computed using a modified shape parameter algorithm. In fact, several experiments containing of three and four assets are worked out showing that the results of the presented method are in good agreement with the literature and could be much more accurate once the shape parameter is chosen carefully.

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Radial basis functions with application to finance: American put option under jump diffusion

Cited by 45 publications

References 14 publications

Hybrid shape parameter strategy for the RBF approximation of vibrating systems

Hybrid shape parameter strategy for the RBF approximation of vibrating systems

Stability and convergence of radial basis function finite difference method for the numerical solution of the reaction–diffusion equations

A Local Radial Basis Function Method for High-Dimensional American Option Pricing Problems

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