Yousuf, M., Khaliq, A.Q.M. and Kleefeld, B. (2012) The Numerical Approximation of Nonlinear Black-Scholes Model for Exotic Path-Dependent American Options with Transaction Cost. International Journal of Computer Mathematics, 89, 1239-1254.
https://doi.org/10.1080/00207160.2012.688115

has been cited by the following article:

• TITLE: Numerical Approximation of Information-Based Model Equation for Bermudan Option with Variable Transaction Costs

  AUTHORS: Matabel Odin, Jane Akinyi Aduda, Cyprian Ondieki Omari

  KEYWORDS: Variable Transaction Costs, Information-Based Model, Finite Difference Method, Bermudan Call Option, Greeks

  JOURNAL NAME: Journal of Mathematical Finance, Vol.13 No.1, February 21, 2023

  ABSTRACT: Non-linear partial differential equations have been increasingly used to model the price of options in the realistic market setting when transaction costs arising in the hedging of portfolios are taken into account. This paper focuses on finding the numerical solution of the non-linear partial differential equation corresponding to a Bermudan call option price with variable transaction costs for an asset under the information-based framework. The finite difference method is implemented to approximate the option price and its Greeks. Numerical examples are presented and the option prices compared to the closed-form solution of the information-based model and the Black Scholes model with zero transaction costs. The results show that the approximated option prices correspond to the analytical solution of the information-based model but are slightly higher than the prices under Black-Scholes model. These findings validate the finite difference method as an efficient way of approximating the information-based non-linear partial differential equation.