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

1) It is possible to borrow and lend cash at a known constant risk-free interest rate.

2) The price follows a geometric Brownian motion with constant drift and volatility.

Also, Black and Scholes make the simplifying assumptions that all securities are perfectly divisible, there are no transaction costs or dividends and there are no restrictions on short selling. These are just simplifications that later, more complicated versions, have worked around. So there are really only two essential assumptions made by quantitative analysts - quants.

Let us begin by considering Black and Scholes' first axiom. A forum discussant, Suzy, writes: