The Chicago Mercantile Exchange, as well as many other options exchanges around the world,
trades options on futures rather than options on spot exchange rates. The volatilities of futures and
spot prices are nearly identical and futures prices converge to spot prices at expiration, so the
differences between options on futures and options on spot exchange rates are minor.18 Equations
6.3 and 6.5 work with forward exchange rates as well as with futures prices.
Solution of the option pricing problem proved to be a turning point in the evolution of finance.
The OPM set the stage for the subsequent introduction and growth of options trading on a variety of
assets, including stocks, bonds, commodities, interest rates, and exchange rates. The OPM also made
a course in stochastic processes a required part of doctoral programs in finance.