A practical finite difference method for the three-dimensional Black–Scholes equation

2016 ◽  
Vol 252 (1) ◽  
pp. 183-190 ◽  
Author(s):  
Junseok Kim ◽  
Taekkeun Kim ◽  
Jaehyun Jo ◽  
Yongho Choi ◽  
Seunggyu Lee ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Three Dimensional ◽  
Black Scholes

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.

scholarly journals A Comparative Study between Implicit and Crank-Nicolson Finite Difference Method for Option Pricing

2020 ◽  
Vol 40 (1) ◽  
pp. 13-27
Author(s):  
Tanmoy Kumar Debnath ◽  
ABM Shahadat Hossain
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Option Pricing ◽  
Difference Method ◽  
Finite Difference Methods ◽  
Put Option ◽  
Black Scholes ◽  
Implicit Finite Difference ◽  
Difference Methods ◽  
Crank Nicolson

In this paper, we have applied the finite difference methods (FDMs) for the valuation of European put option (EPO). We have mainly focused the application of Implicit finite difference method (IFDM) and Crank-Nicolson finite difference method (CNFDM) for option pricing. Both these techniques are used to discretized Black-Scholes (BS) partial differential equation (PDE). We have also compared the convergence of the IFDM and CNFDM to the analytic BS price of the option. This turns out a conclusion that both these techniques are fairly fruitful and excellent for option pricing. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 13-27

Non-Paraxial Split-Step Semi-Vectorial Finite-Difference Method for Three-Dimensional Wide-Angle Beam Propagation

2010 ◽  
Vol 27 (1) ◽  
pp. 014201
Author(s):  
Cheng Hua ◽  
Zang Wei-Ping ◽  
Zhao Zi-Yu ◽  
Li Zu-Bin ◽  
Zhou Wen-Yuan ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Three Dimensional ◽  
Beam Propagation ◽  
Wide Angle
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