In the above Summary, I spoke about the arrival of the rocket scientists and their successors.
Most of the community think that mathematicians are rather curious people, who play around far too seriously with totally incomprehensible things. They often think of us as `bright' but `impractical'. This is a challenge for the applied mathematical profession. In the financial community however, the battle has already been won by those who have contributed significantly to corporate goals, through new or improved products, better risk-management and increased bottom-line profits.
The use of relatively sophisticated mathematics in finance probably began with a dissertation[ 1] on the `Theory of Speculation', submitted to the Sorbonne in 1900 by Louis Bachelier. Bachelier made original contributions to continuous-time stochastic processes and to option-pricing. Option trading is now an immense financial activity. Bachelier also developed the solution to a particular diffusion equation, some five years before Einstein.
Bachelier's work went unnoticed in the financial community until the 1950s. Up until this time, the most sophisticated mathematics had been elementary discounting, to calculate present values of future cash-flows.
In the mid 1950s, Harry Markowitz devised a novel theory of `Portfolio Selection': given a collection of desirable stocks, how much of each one should you hold? Harry formulated this as a mean-variance optimisation problem: the expected return of the portfolio is maximised subject to a penalty on the variability of that return. This was the foundation of `Modern Portfolio Theory' (MPT), for which Harry eventually received a Nobel Prize in 1990. The prize was shared by William Sharpe for the `Capital Asset Pricing Model'. Whilst these theories form the bases for much of the serious institutional investing done around the world, their descriptive abilities have been severely questioned by practitioners in recent times.
Modigliani's and Miller's work on corporate finance in the 1950s and 1960s have also received Nobel Prizes, in 1985 and 1990.
The big leap in mathematical sophistication came in the 1970s with the development of an option-pricing model, by the late Fisher Black and Myron Scholes[ 8], using stochastic calculus. Options are simply the right, but not the obligation, to buy something in the future at a price which is set now. The Chicago Board Options Exchange began trading listed options in April 1973, one month before the publication of the Black-Scholes paper. By 1975, virtually all traders were valuing and hedging their option portfolios, using the Black-Scholes model.