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.
