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

Company, Rafael; Egorova, Vera N.; Jódar, L.; Soleymani, Fazlollah

doi:10.3846/mma.2018.008

Cited by 16 publications

(11 citation statements)

References 26 publications

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“…Meshfree methods (specifically, the localized ones) constructed based on an RBF approximation have been shown to perform better than standard FD methods for option pricing problems in one or more spatial dimensions, see e.g. [9] and the references therein. The main difficulty when using RBF collocation approach is the necessity to invert an ill-conditioned matrix arising due to a global RBF support.…”

Section: )mentioning

confidence: 99%

Pricing foreign exchange options under stochastic volatility and interest rates using an RBF–FD method

Soleymani

Itkin

2019

Journal of Computational Science

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This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented by an Itô's diffusion with time-dependent drift, and with a full matrix of correlations. It is known that prices of FX options in this model can be found by solving an associated backward partial differential equation (PDE). However, it contains non-affine terms, which makes its difficult to solve it analytically. Also, a standard approach of solving it numerically by using traditional finite-difference (FD) or finite elements (FE) methods suffers from the high computational burden. Therefore, in this paper a flavor of a localized radial basis functions (RBFs) method, RBF-FD, is developed which allows for a good accuracy at a relatively low computational cost. Results of numerical simulations are presented which demonstrate efficiency of such an approach in terms of both performance and accuracy for pricing FX options and computation of the associated Greeks.

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Section: )mentioning

confidence: 99%

Pricing foreign exchange options under stochastic volatility and interest rates using an RBF–FD method

Soleymani

Itkin

2019

Journal of Computational Science

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“…Here, in order to reduce the computational burdensome, we apply a similar strategy as in Company et al and d'Halluin et al for both call and put vanilla options and impose the boundaries only for two sides of the computational domain, ie, once s = 0 and

s = s_{\max}

, by considering their differentiation forms along the temporal variable to be zero. This means that

\frac{\partial u}{\partial τ} false(0, v, τ false) ≃ 0,

\frac{\partial u}{\partial τ} false(s_{\max}, v, τ false) ≃ 0 .

…”

Section: Solution Schemementioning

confidence: 99%

“…Here, in order to reduce the computational burdensome, we apply a similar strategy as in Company et al 29…”

Section: Side Conditionsmentioning

confidence: 99%

Asset pricing for an affine jump‐diffusion model using an FD method of lines on nonuniform meshes

Soleymani

Akgül

2018

Math Methods in App Sciences

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We present a novel numerical scheme for the valuation of options under a well‐known jump‐diffusion model. European option pricing for such a case satisfies a 1 + 2 partial integro‐differential equation (PIDE) including a double integral term, which is nonlocal. The proposed approach relies on nonuniform meshes with a focus on the discontinuous and degenerate areas of the model and applying quadratically convergent finite difference (FD) discretizations via the method of lines (MOL). A condition for observing the time stability of the fully discretized problem is given. Also, we report results of numerical experiments.

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“…Tackling on the generalization of the new scheme (16) for interval matrix inversion or the application of such matrix methods in option pricing in order to act as a preconditioner to reduce the ill-conditioning of the large sized matrices occuring in the process of pricing (see, e.g., [31]) could be taken into account as future investigations in this field of study.…”

Section: Summary and Remarksmentioning

confidence: 99%

An Improved Computationally Efficient Method for Finding the Drazin Inverse

Jebreen

Chalco-Cano

2018

Discrete Dynamics in Nature and Society

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Drazin inverse is one of the most significant inverses in the matrix theory, where its computation is an intensive and useful task. The objective of this work is to propose a computationally effective iterative scheme for finding the Drazin inverse. The convergence is investigated analytically by applying a suitable initial matrix. The theoretical discussions are upheld by several experiments showing the stability and convergence of the proposed method.

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

Cited by 16 publications

References 26 publications

Pricing foreign exchange options under stochastic volatility and interest rates using an RBF–FD method

Pricing foreign exchange options under stochastic volatility and interest rates using an RBF–FD method

Asset pricing for an affine jump‐diffusion model using an FD method of lines on nonuniform meshes

An Improved Computationally Efficient Method for Finding the Drazin Inverse

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