Risk Latte - Footnotes in Black-Scholes

Footnotes in Black-Scholes

Rahul Bhattacharya
Mar 24, 2005

In 1965 Fischer Black joined Arthur D Little, a consulting firm near Boston. Here he met Jack Treynor. Treynor is well known for his work in the area of asset pricing (also, known for Treynor ratio) which ultimately led to the same conclusions and results as that of the celebrated capital asset pricing model (CAPM) of William Sharpe, John Lintner and Jan Mossin. Unfortunately, Treynor got very little attention for his work - and certainly didn't get any Nobel prize like Sharpe - because he chose not to publish it in any academic journal.

Anyway, Treynor's greatest contribution may well be to introduce Fischer Black, who had a background in physics and mathematics, to finance; Treynor motivated Black to think about the problem of market equilibrium for risky assets. So great was this motivation that Black and Scholes acknowledged Treynor's role in their journey to find an option pricing formula with the following note on the first page of their now famous paper: "The inspiration for this work was provided by Jack L Treynor (1961a, 1961b). The references to 1961a and 1961b are to Treynor's unpublished manuscripts on CAPM".

Another famous note - a footnote - in Black-Scholes paper referred to the contribution of John Merton. John Merton greatest contribution was to make Finance continuous time, rather than discrete time. It was Merton who showed Black and Scholes that if a stock can be allowed to take many values through time - i.e. the stock moves continuously over infinitesimal intervals of time - the riskless nature of a hedged position dominates over the expected return of the stock, i.e. the riskless return and not the stock's expected return determines the value of the option. Footnote 3 in the Black-Scholes paper refer to this phenomenon and reads "This was pointed out to us by Robert Merton."

The formula is therefore rightly called Black-Scholes-Merton.

(Reference: The above is taken from the excellent book called Puzzles of Finance by Mark P. Kritzman; we strongly recommend all readers to read this book. It is a rare treat!).

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