A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge–Ampère Equation

2019 ◽  
Vol 81 (3) ◽  
pp. 2271-2302 ◽  
Author(s):  
Hao Liu ◽  
Roland Glowinski ◽  
Shingyu Leung ◽  
Jianliang Qian
Keyword(s):  
Finite Element ◽  
Numerical Solution ◽  
Operator Splitting ◽  
Splitting Method ◽  
Three Dimensional ◽  
Operator Splitting Method ◽  
Monge Ampere

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

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 391 ◽  
Author(s):  
Sangkwon Kim ◽  
Darae Jeong ◽  
Chaeyoung Lee ◽  
Junseok Kim
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Operator Splitting ◽  
Splitting Method ◽  
Three Dimensional ◽  
Closed Form Solutions ◽  
Operator Splitting Method ◽  
Black Scholes ◽  
The One

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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