In the summer of 1968, the MIT professor Paul Samuelson proposed to one of his students, Robert C Melton a partnership in order to write a thesis on how to price warrants. Samuelson already published a first attempt elaborating a formula to estimate the value of warrant at a point in time but the weakness was that the assumed expected returns are unknown and unlikely to be constant over time.
After writing the paper together, the new idea was to propose an equilibrium model in which both alpha and beta quantities are determined period by period, by supply and demand, given the risk preferences of investors.
Later, for his PhD work, Melton pioneered writing on the problem of continuous-time stochastic processes. According to his analytical framework, at every immeasurably small instant in time the die that determines the return on an asset is rolled again implying that the return over any limited interval of time is the sum of many rolls.
B for Neo for spelling errors.
ReplyDeleteAt this point, you can start to view the creation of an option pricing model as a race. Samuelson and Merton are on the right track, but not interested enough to pursue the project to its end.
Black has already got the equation that needs to be solved, but he doesn't know how to solve it yet.
Samuelson and Merton were working on warrants. The reason for this is that at the time options were not as common as they are now.
Extra credit to the first person to post a comment describing how a warrant differs from an option. Specifically, for each, do the shares on which the warrant/option is written need to exist before it is written, and is it possible to write them naked.