The Operator Splitting Method for Black-Scholes Equation

Daoud, Yassir; zi, Turgut

doi:10.4236/am.2011.26103

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…The main idea of the OSM is to "divide and conquer" such that we literally divide the multi-dimensional problem into several subproblems and solve in fractional time step [1,2,7,10]. In this two dimensional problem, we split the differential…”

Section: Operator Splitting Methodsmentioning

confidence: 99%

Comparison of Numerical Schemes on Multi-Dimensional Black-Scholes Equations

Jo¹,

Kim²

2013

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, we study numerical schemes for solving multidimensional option pricing problem. We compare the direct solving method and the Operator Splitting Method(OSM) by using finite difference approximations. By varying parameters of the Black-Scholes equations for the maximum on the call option problem, we observed that there is no significant difference between the two methods on the convergence criterion except a huge difference in computation cost. Therefore, the two methods are compatible in practice and one can improve the time efficiency by combining the OSM with parallel computation technique. We show numerical examples including the Equity-Linked Security(ELS) pricing based on either two assets or three assets by using the OSM with the Monte-Carlo Simulation as the benchmark.

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Section: Operator Splitting Methodsmentioning

confidence: 99%

Comparison of Numerical Schemes on Multi-Dimensional Black-Scholes Equations

Jo¹,

Kim²

2013

Bulletin of the Korean Mathematical Society

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“…This method is by decoupling a complex equation in various simpler equations and solving the simpler equation with discretization. Since then, many researchers [4,5,12] have applied OS method to the BS equation.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Numerical Methods (Bi-Cgstab, Os, Mg) for the 2d Black-Scholes Equation

Jeong¹,

Kim²,

Choi³

et al. 2014

The Pure and Applied Mathematics

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In this paper, we present a detailed comparison of the performance of the numerical solvers such as the biconjugate gradient stabilized, operator splitting, and multigrid methods for solving the two-dimensional Black-Scholes equation. The equation is discretized by the finite difference method. The computational results demonstrate that the operator splitting method is fastest among these solvers with the same level of accuracy.

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“…One of the traditional methods both in practice and research for discretizing multidimensional Black-Scholes equations is the Operator Splitting Method (OSM) [1][2][3]. To solve multidimensional Black-Scholes equations, the OSM solves one-dimensional Black-Scholes equations in turn.…”

Section: Introductionmentioning

confidence: 99%

Iterative Speedup by Utilizing Symmetric Data in Pricing Options with Two Risky Assets

Pak

Han²,

Hong

2017

Symmetry

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Abstract:The Crank-Nicolson method can be used to solve the Black-Scholes partial differential equation in one-dimension when both accuracy and stability is of concern. In multi-dimensions, however, discretizing the computational grid with a Crank-Nicolson scheme requires significantly large storage compared to the widely adopted Operator Splitting Method (OSM). We found that symmetrizing the system of equations resulting from the Crank-Nicolson discretization help us to use the standard pre-conditioner for the iterative matrix solver and reduces the number of iterations to get an accurate option values. In addition, the number of iterations that is required to solve the preconditioned system, resulting from the proposed iterative Crank-Nicolson scheme, does not grow with the size of the system. Thus, we can effectively reduce the order of complexity in multidimensional option pricing. The numerical results are compared to the one with implicit Operator Splitting Method (OSM) to show the effectiveness.

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The Operator Splitting Method for Black-Scholes Equation

Cited by 3 publications

References 9 publications

Comparison of Numerical Schemes on Multi-Dimensional Black-Scholes Equations

Comparison of Numerical Schemes on Multi-Dimensional Black-Scholes Equations

Comparison of Numerical Methods (Bi-Cgstab, Os, Mg) for the 2d Black-Scholes Equation

Iterative Speedup by Utilizing Symmetric Data in Pricing Options with Two Risky Assets

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