A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models

Brummelhuis, Raymond; Chan, Ron

doi:10.1080/1350486x.2013.850902

Cited by 20 publications

(20 citation statements)

References 58 publications

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“…with an initial value of u(x, 0) = g(x) := G(e x ) = max{e x − K, 0} , call option max{K − e x , 0} , put option (11) where…”

Section: European Optionsmentioning

confidence: 99%

“…and V Kou (S, T ) is the payoff function (11). For more details on this method, we refer the reader to [31].…”

Section: European Vanilla Optionsmentioning

confidence: 99%

“…However, our method can be easily extended to other contexts in which the basic pricing equation is a PIDE, such as the Carr-Geman-Madan-Yor (CGMY) [15] or variance Gamma (VG) [13,41] Lévy-type models. These models will be addressed in another paper [11]. PIDEs, such as the Merton [44] and Kou Models [34,35], are typically treated using a traditional finite difference method (FDM) or finite element method (FEM).…”

Section: Introductionmentioning

confidence: 99%

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Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme

Chan

Hubbert

2013

Rev Deriv Res

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This paper will demonstrate how European and American option prices can be computed under the jump-diffusion model using the radial basis function (RBF)interpolation scheme. The RBF interpolation scheme is demonstrated by solving an option pricing formula, a onedimensional partial integro-differential equation (PIDE). We select the cubic spline radial basis function and propose a simple numerical algorithm to establish a finite computational range for the improper integral of the PIDE. This algorithm can improve the approximation accuracy of the integral with the application of any quadrature. Moreover, we offer a numerical technique termed cubic spline factorisation to solve the inversion of an ill-conditioned RBF interpolant, which is a well-known research problem in the RBF field. Finally, we numerically prove that in the European case, our RBF-interpolation solution is second-order accurate for spatial variables, while in the American case, it is second-order accurate for spatial variables and first-order accurate for time variables.

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“…with an initial value of u(x, 0) = g(x) := G(e x ) = max{e x − K, 0} , call option max{K − e x , 0} , put option (11) where…”

Section: European Optionsmentioning

confidence: 99%

“…and V Kou (S, T ) is the payoff function (11). For more details on this method, we refer the reader to [31].…”

Section: European Vanilla Optionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme

Chan

Hubbert

2013

Rev Deriv Res

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“…Marazzina et al (2012) for a high-dimensional extension. Radial basis for the Merton and Kou model, American and European options are provided by Chan and Hubbert (2014) and further developed for CGMY models by Brummelhuis and Chan (2014). An implementation that is flexible in the driving model as well as in the option type first of all requires a problem formulation covering the collectivity of envisaged models and options.…”

Section: Introductionmentioning

confidence: 99%

A Flexible Galerkin Scheme for Option Pricing in Lévy Models

Gaß¹,

Glau²

2018

SIAM J. Finan. Math.

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One popular approach to option pricing in Lévy models is through solving the related partial integro differential equation (PIDE). For the numerical solution of such equations powerful Galerkin methods have been put forward e.g. by Hilber et al. (2013). As in practice large classes of models are maintained simultaneously, flexibility in the driving Lévy model is crucial for the implementation of these powerful tools. In this article we provide such a flexible finite element Galerkin method. To this end we exploit the Fourier representation of the infinitesimal generator, i.e. the related symbol, which is explicitly available for the most relevant Lévy models. Empirical studies for the Merton, NIG and CGMY model confirm the numerical feasibility of the method.

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“…We have chosen the Merton jump-diffusion model as a typical case on which to test the present RBF methodology. Comparing with our previous studies [6] and [5], we mainly focus on improving the interpolation accuracy of the option pay-off in order to achieve a higher accuracy of option prices. To acheive this goal, we adopt an adaptive scheme proposed by Driscoll et al [11] and Inverse Multiquadric Radial Basis Function (IMQ).…”

Section: Introductionmentioning

confidence: 99%

Adaptive Radial Basis Function Methods for Pricing Options Under Jump-Diffusion Models

Chan

2016

Comput Econ

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The aim of this paper is to show that option prices in jumpdiffusion models can be computed using meshless methods based on Radial Basis Function (RBF) interpolation instead of traditional meshbased methods like Finite Differences (FDM) or Finite Elements (FEM). The RBF technique is demonstrated by solving the partial integro-differential equation for American and European options on non-dividend-paying stocks in the Merton jump-diffusion model, using the Inverse Multiquadric Radial Basis Function (IMQ). The method can in principle be extended to Lévy-models. Moreover, an adaptive method is proposed to tackle the accuracy problem caused by a singularity in the initial condition so that the accuracy in option pricing in particular for small time to maturity can be improved.

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A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models

Cited by 20 publications

References 58 publications

Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme

Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme

A Flexible Galerkin Scheme for Option Pricing in Lévy Models

Adaptive Radial Basis Function Methods for Pricing Options Under Jump-Diffusion Models

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