Black-Scholes





The following is part of an answer Edward Thorp gave in a recent interview with the Journal of Investment Consulting:

 "... in 1969 I had this options formula, this tool that nobody else had, and I felt an obligation to the [investors in my hedge fund] to basically be quiet about it. The tool was just an internal formula that was known to me and a few other people that I employed. Time passed, and Black and Scholes (1973) published this formula. I remember getting a pre-publication copy in the mail with a letter from Fisher Black saying that he and Scholes were admirers of my work and that they had taken the delta hedging idea of my book Beat the Market (1969) one step further by assuming there was no arbitrage and that this paper presented what they came up with. I thought that this formula had to be the same as what I was running on my computers then, so I plugged it in and drew a graph. However, the graph didn't agree with the graph that I had drawn from my formula, and I [then] realized that I had three formulas, not [just] one. One of the formulas was the Black-Scholes model... I published all three formulas about two or three months later. I was scheduled to give a talk... and I needed something to talk about, so -- almost the same day I received the Black-Scholes paper -- I just wrote up my three formulas and sent them in at that point, knowing that this was no secret any more (Thorp 1973).  

I realized in retrospect that there was no chance I was going to get any recognition for an options formula because I was not part of the economic academic community, and that was extremely important.  I would say there was almost no chance that I could have gotten a paper accepted unless I published it in a math journal somewhere, and then people said years later, "Oh, yeah, this guy found it too?" It wasn't apparent to me that it was as revolutionary, in a broad sense, as it turned out to be. To me, the thing to do seemed to be to protect my investors and their interests and do the best I could for them and just stay ahead in research as well as I could. So that's what I focused on. If you don't publish, you're not going to get credit. 

(Source:  Journal of Investment Consulting, Vol. 12, No. 1, pp. 5-14, 2011)

*****

Offering another point of view is author Aaron Brown:

"Ed did not wait for public options trading in 1973; he began buying and selling warrants (options issued directly by corporations rather than by created exchanges) in the 1960s. He applied the same principles of careful mathematics and controlled risk taking to the market as he had to blackjack and has compiled an unequaled 40-year track record of high-return, low-risk investing.

In coming up with a trading strategy for warrants, Ed discovered a handy formula. A few years later, three finance professors independently came up with their own slight mathematical variant of the same formula. Ed Thorp, Myron Scholes, Robert Merton, and Fischer Black all had almost the same formula, but each had a different reason for believing it was true. Ed showed that it was a way to make money, Scholes that it was required for market efficiency, Merton that it had to be true or there would be arbitrage, and Black that it was required for market equilibrium. Black's insight turned out to be the most important, although it would take him 20 more years to work out its full implications. Merton and Scholes shared a Nobel Prize for their work; Black died by that time or he certainly would have been included. Thorp missed out on the Nobel, be he got rich using the formula, while Merton and Scholes had disastrous personal financial results. Black's dislike of risk kept him from either extreme.

(Source: The Poker Face of Wall Street (Wiley 2006), Author: Aaron Brown)


Ed Thorp had disovered and was profiting from
the Black-Scholes model... 
three years before the eventual Nobel Prize winners