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

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.

Unraveling Market Inefficiencies: Weak Arbitrage and the Information-Based Model for Option Pricing

“…Any numerical approach, like Finite Difference Schemes, Finite Element Methods, and Spectral Methods, can be utilized to obtain the numerical solution for the pricing equation. For the specific case of solving Equation ( 18) using Finite Difference Methods, refer to [42]. This approach can be extended to incorporate the arbitrage measure into the equation.…”

“…Equation ( 16) defines the modified volatility, considering non-increasing exponential costs. [42] provides additional details on how the numerical approximation of the modified volatility is conducted using the explicit finite difference scheme. By considering transaction costs, the model effectively reduces stochastic volatility.…”