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(d
1)-Le
-rTN(d
1-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. d
1 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.