Radial basis function partition of unity operator splitting method for pricing multi-asset American options

Shcherbakov, Victor

doi:10.1007/s10543-016-0616-y

Cited by 30 publications

(12 citation statements)

References 18 publications

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“…In [43], Peherstorfer et al suggested reduced models for pricing basket options with the Black-Scholes and the Heston models. Shcherbakov [48] extended the operator splitting formulation to the radial basis function partition of unity method. A FEM in spatial variables and alternating direction implicit (ADI) method based on the semi-implicit approximation in time variable has been studied in [34].…”

Section: Introductionmentioning

confidence: 99%

Modulus-based Successive Overrelaxation Iteration Method for Pricing American Options with the Two-asset Black–Scholes and Heston's Models Based on Finite Volume Discretization

Gan

Chen

2022

Taiwanese J. Math.

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In this paper we introduce a new numerical method for the linear complementarity problems (LCPs) arising from two-asset Black-Scholes and Heston's stochastic volatility American options pricing. Based on barycenter dual mesh, a class of finite volume method (FVM) is proposed for the spatial discretization, coupled with the backward Euler and Crank-Nicolson schemes are employed for time stepping of the partial differential equations (PDEs). Then, for the resulting time-dependent LCPs are solved by using an efficient modulus-based successive overrelaxation (MSOR) iteration method. Numerical experiments are carried out to verify the efficiency and usefulness of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Modulus-based Successive Overrelaxation Iteration Method for Pricing American Options with the Two-asset Black–Scholes and Heston's Models Based on Finite Volume Discretization

Gan

Chen

2022

Taiwanese J. Math.

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“…In later years, RBFs method has attracted a large number of researchers and practitioners to solve many practical problems [2–14]. RBFs based methods have also been numerically tested for solution of Black–Scholes model and its variants [4, 15–17]. As a truly meshless method, it works for arbitrarily provided data points for initialization and equally effective in higher dimensions due to straight‐forward formulation.…”

Section: Introductionmentioning

confidence: 99%

A hybrid radial basis functions collocation technique to numerically solve fractional advection–diffusion models

Hussain¹,

Haq

2020

Numerical Methods Partial

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In this work, we propose a hybrid radial basis functions (RBFs) collocation technique for the numerical solution of fractional advection-diffusion models. In the formulation of hybrid RBFs (HRBFs), there exist shape parameter (c*) and weight parameter () that control numerical accuracy and stability. For these parameters, an adaptive algorithm is developed and validated. The proposed HRBFs method is tested for numerical solutions of some fractional Black-Sholes and diffusion models. Numerical simulations performed for several benchmark problems verified the proposed method accuracy and efficiency. The quantitative analysis is made in terms of L ∞ , L 2 , L rms , and L rel error norms as well as number of nodes N over space domain and time-step t. Numerical convergence in space and time is also studied for the proposed method. The unconditional stability of the proposed HRBFs scheme is obtained using the von Neumann methodology. It is observed that the HRBFs method circumvented the ill-conditioning problem greatly, a major issue in the Kansa method.

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“…Both of those pricing problems can be formulated as time-dependent multidimensional partial differential equations (PDEs). As a high-order, mesh-free and sparse numerical method from the RBF family, together with the Radial Basis Function Partition of Unity (RBF-PU) method [35,36,33], RBF-FD shows strong potential when it comes to solving multidimensional PDEs. We develop on top of the previous results of using RBF-FD for financial engineering [31,14,24,27,23,22], and use important recent advancement of the RBF-FD approximation in other disciplines [1,8], to build stable, accurate, and fast solvers for multidimensional PDEs in finance.…”

Section: Introductionmentioning

confidence: 99%

Pricing Financial Derivatives using Radial Basis Function generated Finite Differences with Polyharmonic Splines on Smoothly Varying Node Layouts

Milovanović¹

2018

Preprint

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In this paper, we study the benefits of using polyharmonic splines and node layouts with smoothly varying density for developing robust and efficient radial basis function generated finite difference (RBF-FD) methods for pricing of financial derivatives. We present a significantly improved RBF-FD scheme and successfully apply it to two types of multidimensional partial differential equations in finance: a two-asset European call basket option under the Black-Scholes-Merton model, and a European call option under the Heston model. We also show that the performance of the improved method is equally high when it comes to pricing American options. By studying convergence, computational performance, and conditioning of the discrete systems, we show the superiority of the introduced approaches over previously used versions of the RBF-FD method in financial applications.

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Radial basis function partition of unity operator splitting method for pricing multi-asset American options

Cited by 30 publications

References 18 publications

Modulus-based Successive Overrelaxation Iteration Method for Pricing American Options with the Two-asset Black–Scholes and Heston's Models Based on Finite Volume Discretization

Modulus-based Successive Overrelaxation Iteration Method for Pricing American Options with the Two-asset Black–Scholes and Heston's Models Based on Finite Volume Discretization

A hybrid radial basis functions collocation technique to numerically solve fractional advection–diffusion models

Pricing Financial Derivatives using Radial Basis Function generated Finite Differences with Polyharmonic Splines on Smoothly Varying Node Layouts

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