It All Began with Einstein.....

In 1905 Albert Einstein published his three famous papers (actually there were four papers) one of which was on explanation of the statistical mechanics of Brownian motion which produced the now famous heat transfer equation. Black and Scholes used this heat transfer equation – a partial differential equation – to derive the famous option pricing formula.

It was the drift term in the Brownian motion framework that finally resolved the mystery of financial options.

In 1965 Paul A. Samuelson worked on the valuation of warrants that led to a formula of the same general form as that of Black and Scholes, except that Samuelson used for the drift term the expected return of the stock rather than the riskless return which was used later on by Black and Scholes.

The seminal work of Franco Modigliani and Merton Miller in the year 1958, that produced the famous MM hypothesis, and which demonstrated the invariance of a firm’s value to its capital structure and dividend policy inspired Black and Scholes to invoke the principles of no arbitrage to derive their celebrated option pricing formula.

It is anybody’s guess as to what would have happened if Merton Miller had not persuaded the Journal of Political Economy to publish the Black-Scholes manuscript.

It is also anybody’s guess as to what would have happened to our world of finance, and especially financial theory, if Robert C. Merton in the early seventies had not introduced continuous time mathematics to finance. Black-Scholes formula for option pricing is perhaps, the most famous example of continuous time finance. Robert Merton gave Black-Scholes the key insight that is a hedged position is maintained continuously, its return becomes certain.

And finally, Fischer Black and Myron Scholes, in 1973 published their famous paper in the Journal of Political Economy, that used the heat transfer equation of Brownian motion which Einstein had derived, Merton’s insight of a continuous maintained hedged position and MM’s insight of a no-arbitrage portfolio to set up a partial differential equation that is independent of investor’s risk preferences. The solution of this equation is the famous Black-Scholes formula for option pricing.

It is now 2005, a hundred years since it all began..............