European option under a skew version of the GBM model with transaction costs by an RBF method

Abstract

The principal aim of this paper is to calculate the price of the European option under a skew version of the geometric Brownian motion model. To do this, we use the Leland and Kabanov strategy to remove arbitrage opportunities by the delta hedging strategy and adding transaction costs to a portfolio that contains an option and a share of the related stock. This idea generates a partial differential equation (PDE) problem to calculate the option price. To solve the obtained PDE, we use a radial basis functions (RBFs) method and apply the operational matrix of derivative for multiquadric-RBF to reduce the problem to a set of algebraic equations. Finally, we present some numerical results to show the efficiency of the model and the method by considering the Newton–Raphson method and the Bayes information criterion.

Keywords:

• Radial basis function
• SGBM model
• skew Brownian motion
• European option price
• transaction cost

Disclosure statement

No potential conflict of interest was reported by the author(s).