Black-Scholes (thing)

Conceived in 1973 by Myron Scholes, Robert Merton, and Fischer Black, the Black-Scholes Formula is a way to find out how much a call option is worth at any given time. It led to a Nobel Prize for Scholes and Merton in 1997, and operated on the theory that that an investor can precisely replicate the payoff to a call option by buying the underlying stock and financing part of the stock purchase by borrowing. The formula was groundbreaking because it was the first of its kind that actually worked, due to the fact that it eliminated variables that were impossible to measure, such as ‘investor fear’, that other formulas carried.


The formula breaks down like this:
C=SN(d₁)-Le^-rTN(d₁-ðsqrt(T))


C: the current call-option value.

S: the current stock price.

N(d₁): N(d) is the probability that a random draw taken from N will be less than d. d₁ is derived from a different formula that utilizes the price of the stock, the exercise price, the risk-free interest rate, the time to maturity of the call option, and the volatility of the underlying stock price.

L: the exercise price.

e: 2.718, the base for the natural logarithm used for continuous compounding.

^r: the risk free interest rate.

T: the time until the expiration of the call option.

ð: the volatility of the stock.