A new radial basis functions method for pricing American options under Merton's jump-diffusion model

Saib, Aslam Aly El Faidal; Tangman, Désiré Yannick; Bhuruth, Muddun

doi:10.1080/00207160.2012.690034

Cited by 29 publications

(36 citation statements)

References 31 publications

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“…The edge in computational efficiency and ease of implementation of Neumann financial boundary conditions, as compared to the use of the common radial basis function discretisation procedure has been discussed in [46] along with a series of numerical experiments. We employ the following two basis functions in this study:…”

Section: Spatial Discretisation Using Rbfs Based On Dqmentioning

confidence: 99%

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A meshless method for Asian style options pricing under the Merton jump-diffusion model

Saib

Sunhaloo

Bhuruth

2015

International Journal of Computer Mathematics

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In this paper we consider the partial integro-differential equation (PIDE) arising when a stock follows a Poisson distributed jump process, for the pricing of Asian options. We make use of the meshless radial basis functions with differential quadrature (RBFDQ) for approximating the spatial derivatives and demonstrate that the algorithm performs effectively well as compared to the commonly employed finite difference approximations. We also employ Strang splitting with the exponential time integration (ETI) technique to improve temporal efficiency. Throughout the numerical experiments covered in the paper, we show how the proposed scheme can be efficiently employed for the pricing of American style Asian options under both the Black-Scholes and the Merton jump diffusion models.

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Section: Spatial Discretisation Using Rbfs Based On Dqmentioning

confidence: 99%

“…However, the method has been shown to experience oscillations due to a lack of L 0 stability [19] and we therefore choose the exponential time integration scheme as an efficient alternative [46,52].…”

Section: Time Integrationmentioning

confidence: 99%

A meshless method for Asian style options pricing under the Merton jump-diffusion model

Saib

Sunhaloo

Bhuruth

2015

International Journal of Computer Mathematics

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“…For the spatial discretization a uniform S-grid is used except in [45,37] where a non-uniform grid is chosen to have a more refined grid near the strike. In a second group of papers [26,27,38,8,24,22,7,23] the PIDE is transformed into a PIDE for the option price as a function of the log-returns. The differential operator has in that case constant coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…This penalty method is used in, e.g., [45,40,9] and is simple and efficient but only first order implying slow convergence. We will apply the operator splitting method as in, e.g., [39,27,38,23] and introduced by [21] in the context of American option pricing. Its advantage is that no fixed point iteration techniques are needed at each time step in the discretized problem and that it has a a second-order convergence rate.…”

Section: Introductionmentioning

confidence: 99%

“…Recently radial basis functions (RBFs) methods have gained a lot of interest. In [15,19,38,3,7] meshfree methods based on an RBF approximation have been shown to perform better than finite difference methods for option pricing problems in one or more spatial dimensions. However, the RBF collocation method in these papers is a global one and leads to a dense linear system which suffers from ill-conditioning.…”

Section: Introductionmentioning

confidence: 99%

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An RBF–FD method for pricing American options under jump–diffusion models

Haghi

Mollapourasl

Vanmaele

2018

Computers & Mathematics with Applications

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American option prices under jump-diffusion models are determined as solutions to partial integro-differential equations (PIDE). In this paper a new combination of a time and spatial discretization applied to a linear complementary formulation (LCP) of the free boundary PIDE is proposed. First a coordinate stretching transformation is performed to the asset price so that the computation of the prices can be focused on regions of real interest instead of on the whole solution domain. An implicit-explicit time discretization applied to the reformulated LCP on a uniform temporal grid is followed by a spatial discretization to get a fully discrete system. The radial basis function (RBF) finite difference method is a local method resulting in a sparse linear system in contrast to global RBF-methods which lead to ill-conditioned dense matrix systems. For the corresponding European option we prove consistency, stability and second-order convergence in a discrete L2-norm. We derive mild conditions for the model parameters under which these results hold. Numerical experiments are performed with European and American options, and a comparison with numerical results available in the literature illustrates the accuracy and efficiency of the proposed algorithm.

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An ETD method for multi‐asset American option pricing under jump‐diffusion model

Company

Egorova

Jódar

2023

Math Methods in App Sciences

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In this paper, we propose a numerical method for American multi-asset options under jump-diffusion model based on the combination of the exponential time differencing (ETD) technique for the differential operator and Gauss-Hermite quadrature for the integral term. In order to simplify the computational stencil and improve characteristics of the ETD-scheme mixed derivative eliminating transformation is applied. The results are compared with recently proposed methods.

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A new radial basis functions method for pricing American options under Merton's jump-diffusion model

Cited by 29 publications

References 31 publications

A meshless method for Asian style options pricing under the Merton jump-diffusion model

A meshless method for Asian style options pricing under the Merton jump-diffusion model

An RBF–FD method for pricing American options under jump–diffusion models

An ETD method for multi‐asset American option pricing under jump‐diffusion model

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