  The Black-Scholes Option pricing model (BSOPM) has long been in use for
valuation of equity options to find the prices of stocks. In this work, using
BSOPM, we have come up with a comparative analytical approach and numerical
technique to find the price of call option and put option and considered these
two prices as buying price and selling price of stocks of frontier markets so
that we can predict the stock price (close price). Changes have been made to
the model to find the parameters strike price and the time of expiration for
calculating stock price of frontier markets. To verify the result obtained
using modified BSOPM we have used machine learning approach using the software
Rapidminer, where we have adopted different algorithms like the decision tree,
ensemble learning method and neural network. It has been observed that, the
prediction of close price using machine learning is very similar to the one
obtained using BSOPM. Machine learning approach stands out to be a better
predictor over BSOPM, because Black-Scholes-Merton equation includes risk and
dividend parameter, which changes continuously. We have also numerically
calculated volatility. As the prices of the stocks goes high due to
overpricing, volatility increases at a tremendous rate and when volatility
becomes very high market tends to fall, which can be observed and determined
using our modified BSOPM. The proposed modified BSOPM has also been explained
based on the analogy of Schrodinger equation (and heat equation) of quantum
physics.
