Open AccessA Comparative Study between Implicit and Crank-Nicolson Finite Difference Method for Option Pricing
Author(s) -
Tanmoy Kumar Debnath,
Abm Shahadat Hossain
Publication year - 2020
Publication title -
ganit
Language(s) - English
Resource type - Journals
eISSN - 2224-5111
pISSN - 1606-3694
DOI - 10.3329/ganit.v40i1.48192
Subject(s) - crank–nicolson method , finite difference methods for option pricing , mathematics , finite difference method , valuation of options , finite difference , black–scholes model , discretization , partial differential equation , convergence (economics) , valuation (finance) , finite difference coefficient , mathematical optimization , econometrics , mathematical analysis , finite element method , economics , finance , mixed finite element method , physics , thermodynamics , volatility (finance) , economic growth
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