Black-Scholes: Robert Merton on the Options Pricing Model

It would take the whole magazine to explain this formula.

1973 Fischer Black, Myron Scholes, and Robert Merton publish papers on the Black-Scholes formula for valuing options.

I bought my first share of stock when I was 10 years old. I came from an academic family. There wasn’t much money. Where I went to trade, they kind of adopted me, because I was a kid. That’s when I first learned about convertible bonds. I would trade at 6:30 a.m. at Caltech. I traded over-the-counter options, especially warrants, and convertible bonds, even though I didn’t know what I was doing. I went to MIT for grad school. I did a joint paper with Paul Samuelson on warrant pricing. That dealt with the option pricing problem, but we didn’t quite crack it.

At MIT, Scholes and Black were working, and I was working. We were in a rivalry. As Myron said, “We don’t tell Merton everything, because he’s a competitor.” Who gets it right wins, period. At the same time, it’s cooperative. You all have an interest in figuring out how it works. That’s a tension that always exists within research. It was a healthy competition, one of mutual respect.

Scholes’s and Black’s insight, which was a critical insight, was that hedging an option removes its systematic risk. At first I said, “That’s impossible.” But I looked into it. I went back to them and said, “You guys are absolutely right, but for the wrong reason.” The hedge removes all risk. There are two derivations of the formula: theirs and mine. They were nice enough to include mine in their paper. They put in a single footnote that said basically, “Bob Merton gave this to us.” Black, to the end of his life, thought their solution was more elegant. But the replication system, the one I came up with, has caught on. Later I named the model the Black-Scholes model, in an appendix to a Samuelson paper. It seems a little pretentious to name something in your own name.

An option is essentially financial insurance. It’s the right but not the obligation to take some kind of action in the future, like to buy or sell an asset. Holding an option can be very valuable. The theory describes not just the price of an option but what a low-cost intermediary or institution could manufacture the options for. It’s kind of a production theory for finance instruments. I can come up with a completely new instrument and calculate what it should be worth. That had an important effect on the speed of innovation. Black-Scholes filled a need. In the 1970s we had stagflation; we had Bretton Woods coming apart, currencies bouncing around, OPEC. It was, “Oh, my God!” The stock market fell 50 percent in real [inflation-adjusted] terms in 18 months.

In the old options market, dealers ran ads in the newspaper with teasers, with posted prices for something that should change value by the minute. Can you imagine posting prices in the newspaper? It’s just bizarre. There were the damnedest kinds of things being used to price options—cube-root rules and stuff that came out of thin air.

Within months they all adopted our model. All the students we produced at MIT, I couldn’t keep them in-house; they were getting hired by Wall Street. Texas Instruments created a specialized calculator with the formula in it for people in the pits. Scholes asked if we could get royalties. They said, “No.” Then he asked if we could get a free one, and they said, “No.”

Now the formula is used everywhere. If you have a mortgage, your right to prepay is an option. Your right to default and turn over the house to the lender if it’s underwater is an option. Every simple mortgage has these two options embedded in it. Seven hundred trillion dollars of this stuff is sloshing around the earth.

People say, “Imagine if you got a penny every time somebody used the Black-Scholes formula.” In every way we did better by putting it in the public domain, which is what we planned to do anyway. Had it not been in the public domain, it might never have been adopted. —As told to Peter Coy

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