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.
