scholarly journals Asymptotic expansion of solutions to the Black–Scholes equation arising from American option pricing near the expiry

2017 ◽  
Vol 311 ◽  
pp. 11-37 ◽  
Author(s):  
Seyed-Mohammad-Mahdi Kazemi ◽  
Mehdi Dehghan ◽  
Ali Foroush Bastani
Keyword(s):  
Asymptotic Expansion ◽  
Option Pricing ◽  
American Option ◽  
American Option Pricing ◽  
Black Scholes ◽  
Asymptotic Expansion Of Solutions

A fractional reduced differential transform method for solving time fractional Black Scholes American option pricing equation

2021 ◽  
Vol 30 (1) ◽  
pp. 1-10
Author(s):  
MANZOOR AHMAD ◽  
RAJSHREE MISHRA ◽  
RENU JAIN
Keyword(s):  
Option Pricing ◽  
American Option ◽  
Differential Transform Method ◽  
American Option Pricing ◽  
Transform Method ◽  
Put Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Differential Transform ◽  
Reduced Differential Transform Method

In this paper, fractional reduced differential transform method (FRDTM) is operated to solve time fractional Black-Scholes American option pricing equation paying no dividends.The Black-Scholes model plays a significant role in the evaluation of European or American call and put options. The advantage of the proposed method to other existing methods is that it finds the solution without discretization or transformation. While using this method, no recommended assumptions are needed and hence the computational work reduces to a greater extent. Numerical experiments prove that the proposed method is efficient and valid for obtaining the solution of time fractional Black-Scholes equation governing American options. This method proves to be powerful for solving general fractional order partial differential equations (PDEs) existing in the field of Science, Engineering and other related fields.

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