Author(s)

Matabel Odin^1*, Jane Akinyi Aduda², Cyprian Ondieki Omari³

¹Department of Mathematics, Pan African University Institute for Basic Sciences, Technology and Innovation (PAUSTI), Nairobi, Kenya.
²Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi, Kenya.
³Department of Statistics and Actuarial Sciences, Dedan Kimathi University of Technology (DeKUT), Nyeri, Kenya.

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.

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

Odin, M. , Aduda, J. and Omari, C. (2023) Numerical Approximation of Information-Based Model Equation for Bermudan Option with Variable Transaction Costs. Journal of Mathematical Finance, 13, 89-111. doi: 10.4236/jmf.2023.131006.