Introduction to Corporate Finance

ParT 2: ValuaTION, rISk aNd reTurN

8-4b THe BlaCk–SCHOleS MOdel

In 1973, Fischer Black and Myron Scholes published what might fairly be called a trillion-dollar research

paper. Their research produced, for the first time, a formula that traders could use to calculate the value

of call options – a path-breaking discovery that had eluded researchers for decades. Black and Scholes

did not have to wait long to see whether their formula would have an effect in financial markets. That

same year, options began trading in the United States on the newly formed Chicago Board Options

Exchange (CBOE). Traders on the floor of the options exchange used handheld calculators that were

programmed with the Black-Scholes formula. From that beginning, trading in options exploded over the

next two decades, hence the trillion-dollar moniker given to the original research paper.^14

14 For this achievement, Myron Scholes won the Nobel Prize in Economics in 1997, an honour he shared with Robert Merton, another researcher

who made seminal contributions to options research. Fischer Black undoubtedly would have been a co-recipient of the award had he not died

in 1995. Indeed, unusually, Black was mentioned in the Prize citation even though under the Nobel rules, he could not be a winner due to his

earlier death.

FIGure 8.8 MULTISTAGE BINOMIAL TREES

The binomial model can be modified to allow for multiple share price movements throughout the life of an option. The more

movements we build into the model, the finer the grid of possible share prices when the option expires.

$55.00

$58.75

$51.25

$55.00

$47.50

$62.50

$58.75

$51.25

$66.25

$43.75

$62.50

$55.00

$70.00

$47.50

$40.00

$55.00

$62.50

$47.50

$70.00

$40.00

$55.00