Numerical Investigation of Option Pricing Using Blackscholes-Merton Partial Differential Equation with Transaction Cost and Non-Constant Volatility

Abstract

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 due to volatility and unpredictable market forces. Black-Scholes-Merton model has so far been proved to be robust and significant tool for the valuation of an option. To achieve more reliable and accurate price estimates, this study investigated the effects of transaction cost and non-constant volatility 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 was then used to approximate the solution to the Black-Scholes-Merton model equation describing the value of an option with boundary conditions. The simulation was done with the aid of MATLAB software program. The effects of incorporating transaction cost and non-constant volatility on the two assets prices on the value of an option using Black-Scholes-Merton Partial Differential Equation were determined. It was established that as the volatility increases, the call and put option values also increase. Further, the study established that as transaction cost increases, the call and put option values decrease. The effects of incorporating transaction cost and non-constant volatility on the values of call and put option were shown in tabular form and presented graphically. These results will be 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.