Open AccessNumerical Solution of European and American Option with Dividends using Finite Difference Methods
Author(s) -
Kedar Nath Uprety,
Ganesh Prasad Panday
Publication year - 2020
Publication title -
vaijñānika jagat
Language(s) - English
Resource type - Journals
ISSN - 1996-8949
DOI - 10.3126/sw.v13i13.30540
Subject(s) - discretization , mathematics , partial differential equation , numerical analysis , black–scholes model , valuation of options , dividend , relaxation (psychology) , mathematical analysis , finance , economics , econometrics , volatility (finance) , social psychology , psychology
Numerical methods form an important part of the pricing of financial derivatives where there is no closed form analytical formula. Black-Scholes equation is a well known partial differential equation in financial mathematics. In this paper, we have studied the numerical solutions of the Black-Scholes equation for European options (Call and Put) as well as American options with dividends. We have used different approximate to discretize the partial differential equation in space and explicit (Forward Euler’s), fully implicit with projected Successive Over-Relaxation (SOR) algorithm and Crank-Nicolson scheme for time stepping. We have implemented and tested the methods in MATLAB. Finally, some numerical results have been presented and the effects of dividend payments on option pricing have also been considered.