The most important event in the development of
computational finance was the publication
in 1973 of the
*Black-Scholes option pricing formula*.
Developed by Fischer Black and Myron
Scholes, with substantial assistance
by Robert Merton, this formula tells
how to compute the price of an option
to buy a share of stock at a future date
but at a price agreed upon before that date.
While such options are important in their
own right, the more important aspect
of the work of Black, Merton and Scholes
was that it initiated a whole body of work
on how to price
*
derivative securities,
*
securities whose price is
*
derived
*
from the price of some other security.
(The price of a stock option is "derived"
from the price of the underlying stock
on which the option is written
via the Black-Scholes formula.)
Scholes and Merton won the 1997 Nobel Prize
in Economics for their work. Fischer Black
would no doubt have shared in this prize
if he had not died two years earlier.

The Black-Scholes formula says the price of an option
to buy a stock at a price *K* at time *T* units in
the future should be

where

and

In this formula, *N* is the standard cumulative normal
distribution (the bell-shaped curve), given by

*S* is the
*
stock price
*
at the time the option is priced, *r* is the
*
interest rate
*
at which money can be borrowed, and the critical parameter
σ
is the
*
volatility
*
of the stock, a measure
of how risky the stock is. The derivation of the
formula requires a good understanding of calculus
and probability theory. Its use as a guide
for buying and selling options requires
one to also understand financial markets.
The discovery of the Black-Scholes formula facilitated
the growth in options trading. It also sparked
the search for similar formulas for more complicated
derivative securities, and this has revolutionized
the finance industry.

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