A quasi-radial basis functions method for American options pricing

Hon, Y.C.

doi:10.1016/s0898-1221(01)00302-9

Cited by 103 publications

(102 citation statements)

References 20 publications

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“…Kansa's method was recently extended to solve various ordinary and partial differential equations including 1D nonlinear Burgers' equation [19] with shock wave, shallow water equations for tide and currents simulation [20], heat transfer problems [17], KdV equation [21], and free boundary problems [22,23]. Fasshauer [24] later modified Kansa's method to a Hermite type collocation method for the solvability of the resultant collocation matrix.…”

Section: Introductionmentioning

confidence: 99%

A numerical method for solving the hyperbolic telegraph equation

Dehghan

Shokri

2007

Numerical Methods Partial

195

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Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this article, we propose a numerical scheme to solve the one-dimensional hyperbolic telegraph equation using collocation points and approximating the solution using thin plate splines radial basis function. The scheme works in a similar fashion as finite difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme.

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Section: Introductionmentioning

confidence: 99%

A numerical method for solving the hyperbolic telegraph equation

Dehghan

Shokri

2007

Numerical Methods Partial

195

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“…The criteria concerned in these experiments include the number of iterations, computational time and Root Mean Square Error (RMSE). The parameters used in these experiments are taken from Hon (2002) whereby K = 100, r = 0.1, σ = 0.30, T = 1(year), s∈ [e −5 , e 7 ]. The matrix sizes tested are 512, 1024, 2048, 4096, 8192 and 16384.…”

Section: Resultsmentioning

confidence: 99%

“…The error tolerance ε = 10 −10 is selected for the convergence test. For comparison, the numerical results obtained will be compared with the results of Binomial method (Hon, 2002). Table 1 presents the experimental results.…”

Section: Resultsmentioning

confidence: 99%

Quarter-Sweep Projected Modified Gauss-Seidel Algorithm Applied to Linear Complementarity Problem

Koh¹

2010

American Journal of Applied Sciences

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Problem statement: Modified Gauss-Seidel (MGS) was developed in order to improve the convergence rate of classical iterative method in solving linear system. In solving linear system iteratively, it takes longer time when many computational points involved. It is known that by applying quarter-sweep iteration scheme, it can decrease the computational operations without altering the accuracy. In this study, we investigated the effectiveness of the new Quarter-Sweep Projected Modified Gauss-Seidel (QSPMGS) iterative method in solving a Linear Complementarity Problem (LCP). Approach: The LCP we looked into is the LCP arise in American option pricing problem. Actually, American option is a Partial Differential Complementarity Problem (PDCP). By using full-, half-and quarter-sweep Crank-Nicolson finite difference schemes, the problem was reduced to Linear Complementarity Problem (LCP). Results: Several numerical experiments were carried out to test the effectiveness of QSPMGS method in terms of number of iterations, computational time and Root Mean Square Error (RMSE). Comparisons were made with full-, half-and quarter-sweep algorithm based on Projected Gauss-Seidel (PGS) and Projected Modified Gauss-Seidel (PMGS) methods. Thus, the experimental results showed that the QSPMGS iterative method has the least number of iterations and shortest computational time. The RMSE of all tested methods are in good agreement. Conclusion: QSPMGS is the most effective among the tested iterative methods in solving LCP whereby it is fastest and the accuracy remains the same.

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“…Such a splitting scheme introduces an error, which turns out to be sufficiently small to not influence the order of the time integration scheme [10]. It is also possible in each time step to ignore the free boundary and then apply the American constraint explicitly [7], but this approach reduces the order of the time integration, while the splitting method uses the auxiliary variable λ to improve the accuracy. More details about the operator splitting method for pricing American options can be found in [10] and references therein.…”

Section: The Operator Splitting Methodsmentioning

confidence: 99%

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

Shcherbakov

2016

Bit Numer Math

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PostprintThis is the accepted version of a paper published in BIT Numerical Mathematics. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination. AbstractThe operator splitting method in combination with finite differences has been shown to be an efficient approach for pricing American options numerically. Here, the operator splitting formulation is extended to the radial basis function partition of unity method. An approach that has previously often been used together with radial basis function methods to deal with the free boundary arising in American option pricing is to solve a penalised version of the Black-Scholes equation. It is shown that the operator splitting technique outperforms the penalty approach when used with the radial basis function partition of unity method. Numerical experiments are performed for one, two and three underlying assets. The advantage of the operator splitting technique grows with the number of dimensions.

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A quasi-radial basis functions method for American options pricing

Cited by 103 publications

References 20 publications

A numerical method for solving the hyperbolic telegraph equation

A numerical method for solving the hyperbolic telegraph equation

Quarter-Sweep Projected Modified Gauss-Seidel Algorithm Applied to Linear Complementarity Problem

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

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