The Black-Scholes formula was developed by Fischer Black and Myron Scholes in the 1970s. The Black-Scholes formula is a stochastic partial differential equation which estimates the price of an option. The main idea behind the formula is the delta neutral portfolio. They created the theoretical delta neutral portfolio to reduce the uncertainty involved.
This was a necessary step to be able to come to the analytical formula, which we'll cover in this section. The following are the assumptions made under the Black-Scholes formula:
No arbitrage
Possible to borrow money at a constant risk-free interest rate (throughout the holding of the option)
Possible to buy, sell, and shortlist fractional amounts of underlying assets
No transaction costs
Price of the underlying asset follows a Brownian motion, constant drift, and volatility
No dividends paid from underlying security
The simplest of the two variants is the one for call options. First, the stock price is scaled using...