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

In this paper, we briefly review the finite difference method (FDM) for the Black–Scholes (BS) equations for pricing derivative securities and provide the MATLAB codes in the Appendix for the one-, two-, and three-dimensional numerical implementation. The BS equation is discretized non-uniformly in space and implicitly in time. The two- and three-dimensional equations are solved using the operator splitting method. In the numerical tests, we show characteristic examples for option pricing. The computational results are in good agreement with the closed-form solutions to the BS equations.

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“…, N y . Now, we apply the operator splitting (OS) method [22,23] to solve Equation (5). We consider the following three discrete equations:…”

Section: By Changing the Variable Withmentioning

confidence: 99%

Finite Difference Method for the Multi-Asset Black–Scholes Equations

et al. 2020

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“…This results in a constant value of φ in the direction normal to the surface, thus the Laplace-Beltrami operator can be replaced by the standard Laplacian operator. In addition, we split the equation into one linear and two nonlinear subequations [17,18], where the nonlinear subequations are independent of spatial derivatives and thus are ordinary differential equations and have closed-form solutions. Therefore, we only solve the linear subequation on the narrow band domain using the Crank-Nicolson method.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Pattern Formation on Surfaces Using an Efficient Linear Second-Order Method

Lee¹

2019

Symmetry

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We present an efficient linear second-order method for a Swift-Hohenberg (SH) type of a partial differential equation having quadratic-cubic nonlinearity on surfaces to simulate pattern formation on surfaces numerically. The equation is symmetric under a change of sign of the density field if there is no quadratic nonlinearity. We introduce a narrow band neighborhood of a surface and extend the equation on the surface to the narrow band domain. By applying a pseudo-Neumann boundary condition through the closest point, the Laplace-Beltrami operator can be replaced by the standard Laplacian operator. The equation on the narrow band domain is split into one linear and two nonlinear subequations, where the nonlinear subequations are independent of spatial derivatives and thus are ordinary differential equations and have closed-form solutions. Therefore, we only solve the linear subequation on the narrow band domain using the Crank-Nicolson method. Numerical experiments on various surfaces are given verifying the accuracy and efficiency of the proposed method.

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“…• In the first step, the D-CFPR matrix R D = D ij n×n , is constructed for n criteria, by considering the system as an input using Equations (9)- (12).…”

Section: Evaluating the Risk Criteria Weight Using D-anpmentioning

confidence: 99%

“…In comparison to other sectors, construction projects encounter more risks due to uncertainties occurring because of various construction practices, working conditions, mixed cultures and political conditions between host and home countries [9][10][11][12]. Thus, in this scenario, risk management can be considered a vital part of the decision-making process in construction projects.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid MCDM Technique for Risk Management in Construction Projects

et al. 2018

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Multi-stakeholder based construction projects are subject to potential risk factors due to dynamic business environment and stakeholders' lack of knowledge. When solving project management tasks, it is necessary to quantify the main risk indicators of the projects. Managing these requires suitable risk mitigation strategies to evaluate and analyse their severity. The existence of information asymmetry also causes difficulties with achieving Pareto efficiency. Hence, to ensure balanced satisfaction of all participants, risk evaluation of these projects can be considered as an important part of the multi-criteria decision-making (MCDM) process. In real-life problems, evaluation of project risks is often uncertain and even incomplete, and the prevailing methodologies fail to handle such situations. To address the problem, this paper extends the analytical network process (ANP) methodology in the D numbers domain to handle three types of ambiguous information's, viz. complete, uncertain, and incomplete, and assesses the weight of risk criteria. The D numbers based approach overcomes the deficiencies of the exclusiveness hypothesis and completeness constraint of Dempster-Shafer (D-S) theory. Here, preference ratings of the decision matrix for each decision-maker are determined using a D numbers extended consistent fuzzy preference relation (D-CFPR). An extended multi-attributive border approximation area comparison (MABAC) method in D numbers is then developed to rank and select the best alternative risk response strategy. Finally, an illustrative example from construction sector is presented to check the feasibility of the proposed approach. For checking the reliability of alternative ranking, a comparative analysis is performed with different MCDM approaches in D numbers domain. Based on different criteria weights, a sensitivity analysis of obtained ranking of the hybrid D-ANP-MABAC model is performed to verify the robustness of the proposed method.

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

Cited by 6 publications

References 17 publications

Finite Difference Method for the Multi-Asset Black–Scholes Equations

Finite Difference Method for the Multi-Asset Black–Scholes Equations

Numerical Simulation of Pattern Formation on Surfaces Using an Efficient Linear Second-Order Method

A Hybrid MCDM Technique for Risk Management in Construction Projects

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