Weak Galerkin finite element method for valuation of American options

Zhang, Ran; Song, Haiming; Luan, Nana

doi:10.1007/s11464-014-0358-6

Cited by 14 publications

(8 citation statements)

References 22 publications

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“…In this section, we mainly introduce the optimal exercise boundary of American options. A derivation of this part can be found in [35]. For completeness, we outline the main process as follows.…”

Section: The Optimal Exercise Boundarymentioning

confidence: 99%

Spectral Method for the Black-Scholes Model of American Options Valuation

Song

Zhang

Tian³

2014

JMS

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In this paper, we devote ourselves to the research of numerical methods for American option pricing problems under the Black-Scholes model. The optimal exercise boundary which satisfies a nonlinear Volterra integral equation is resolved by a high-order collocation method based on graded meshes. For the other spatial domain boundary, an artificial boundary condition is applied to the pricing problem for the effective truncation of the semi-infinite domain. Then, the front-fixing and stretching transformations are employed to change the truncated problem in an irregular domain into a one-dimensional parabolic problem in [−1,1]. The Chebyshev spectral method coupled with fourth-order Runge-Kutta method is proposed for the resulting parabolic problem related to the options. The stability of the semi-discrete numerical method is established for the parabolic problem transformed from the original model. Numerical experiments are conducted to verify the performance of the proposed methods and compare them with some existing methods.

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Section: The Optimal Exercise Boundarymentioning

confidence: 99%

Spectral Method for the Black-Scholes Model of American Options Valuation

Song

Zhang

Tian³

2014

JMS

Self Cite

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“…In general, the closed-form solution for pricing options is not available due to the complexity and diversity of their structures. Therefore, one needs to approximate the solution using numerical methods, such as Monte Carlo simulation (MCS) [2,3], the lattice method [4], the finite difference method (FDM) [5][6][7], finite element method [8,9], or finite volume method [10] for the Black-Scholes (BS) equation. MCS has the advantage of a lower calculation cost and less dependence on dimensions.…”

Section: Introductionmentioning

confidence: 99%

Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method

et al. 2020

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In this article, we propose a super-fast computational algorithm for three-asset equity-linked securities (ELS) using the finite difference method (FDM). ELS is a very popular investment product in South Korea. There are one-, two-, and three-asset ELS. The three-asset ELS is the most popular financial product among them. FDM has been used for pricing the one- and two-asset ELS because it is accurate. However, the three-asset ELS is still priced using the Monte Carlo simulation (MCS) due to the curse of dimensionality for FDM. To overcome the limitation of dimension for FDM, we propose a systematic non-uniform grid with an explicit Euler scheme and an optimal implementation of the algorithm. The computational time is less than 6 s. We perform standard ELS option pricing and compare the results from the fast FDM with the ones from MCS. The computational results confirm the superiority and practicality of the proposed algorithm.

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“…For the spatial discretization of the PIDE typically a traditional finite difference method (FDM) is applied as in [6,26,27,39,40] or a finite element method (FEM) as in [20,29,49] for the PDE case or a finite volume method as in [48,18]. There are several other numerical methods available in the literature to solve the governing equation.…”

Section: Introductionmentioning

confidence: 99%

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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Weak Galerkin finite element method for valuation of American options

Cited by 14 publications

References 22 publications

Spectral Method for the Black-Scholes Model of American Options Valuation

Spectral Method for the Black-Scholes Model of American Options Valuation

Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method

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

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