Mathematical Investigation of Option Pricing using Black- Scholes-Merton Partial Differential Equation with Transaction Cost

Over the years studies have been done on option pricing valuation. The world market economies have experienced tremendous asset price fluctuations since 1980s. For this reason, efforts have been directed towards developing reliable and more accurate option pricing models. Black-Scholes-Merton model has so far been proved to be the most powerful and significant tool for the valuation of an option. However, its assumption of zero transaction cost on asset pricing yields inaccurate option values. The study investigates the effects of transaction cost on call and put option of an asset price using a two-dimensional Black-Scholes-Merton partial differential equation. The Dufort-Frankel Finite Difference Method is used to approximate the solution to the BSM model equation describing the value of an option with boundary conditions. The simulation is done with the aid of MATLAB software program. The effects of incorporating transaction cost on the two assets prices on the value of an option using BSMPDE are determined. From the study, it is established that as transaction cost increases, the call and put option values decrease. The effects of incorporating transaction cost on the values of call and put option are shown in tabular form and graphically. These results are useful to the investors in computing possible returns on investment based on more accurate asset pricing and to the government on policy formulation in controlling prices in stock exchange market.