MBACalculator.com Black Scholes Option Pricing Model - Stock Equilibrium

BlackScholes model
The Black-Scholes model of the market for an equity makes the following explicit assumptions:

It is possible to borrow and lend cash at a known constant risk-free interest rate.
The price follows a geometric Brownian motion with constant drift and volatility.
There are no transaction costs.
The stock does not pay a dividend (see below for extensions to handle dividend payments).
All securities are perfectly divisible (i.e. it is possible to buy any fraction of a share).
There are no restrictions on short selling.
The model treats only European-style options. From these ideal conditions in the market for an equity (and for an option on the equity), the authors show that the value of an option (the Black-Scholes formula) varies only with the stock price and time to expiry. "Thus it is possible to create a hedged position, consisting of a long position in the stock and a short position in [calls on the same stock], whose value will not depend on the price of the stock."[1]