Explicit Finite Difference Methods and its Stability on Black-Scholes Model

2010 ◽  
Author(s):  
Lu Huapu ◽  
Yu Xinxin ◽  
Li Yue ◽  
Zhao Xiaoqiang ◽  
Dai Shuai
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Difference Methods ◽  
Explicit Finite Difference

On the Solution of the Diffusion Equations by Numerical Methods

1966 ◽  
Vol 88 (4) ◽  
pp. 421-427 ◽  
Author(s):  
H. Z. Barakat ◽  
J. A. Clark
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Present Method ◽  
Finite Difference Methods ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Approximation Procedure ◽  
Implicit Methods ◽  
Difference Methods ◽  
Explicit Finite Difference

An explicit-finite difference approximation procedure which is unconditionally stable for the solution of the general multidimensional, nonhomogeneous diffusion equation is presented. This method possesses the advantages of the implicit methods, i.e., no severe limitation on the size of the time increment. Also it has the simplicity of the explicit methods and employs the same “marching” type technique of solution. Results obtained by this method for several different problems are compared with the exact solution and with those obtained by other finite-difference methods. For the examples solved the numerical results obtained by the present method are in closer agreement with the exact solution than are those obtained by the other methods.

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

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