Assumptions of the Black-Scholes Option Pricing Model

No riskless arbitrage opportunity exists.

There are zero transaction costs.

There are no restrictions to short selling of the underlying security.

You can buy or sell any quantity of the underlying security, even a fraction (e.g. 0.1843 shares).

You can borrow or lend cash, in any quantity, at a constant risk-free interest rate (this risk-free interest rate is one of the parameters entering the calculation of option prices).

Future direction of the price of the underlying security canâ€™t be predicted. The price makes a “random walk”. This also means that: