# Black-Scholes-Merton: A 40-year revolution in finance

### Professor Robert Merton discusses the transformative financial model that won him the Nobel Memorial Prize in Economic Sciences

October 2, 2013

*MIT Sloan this month celebrates the 40th anniversary of the Black-Scholes-Merton options pricing model. Created by MIT Sloan professors Robert Merton and Myron Scholes, along with Fischer Black, the model is considered a hallmark of modern finance. In a recent interview, Merton recalled teaching the as-yet-unpublished model at MIT Sloan, explained how he almost missed his Nobel Prize phone call, and discussed the model’s immediate and dramatic impact on the financial industry.*

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The offer came from Franco Modigliani, himself a future Nobel laureate: “How would you like to teach at the Sloan School here?”

Robert Merton, a young economist just finishing his PhD at MIT, had job offers. The MIT Department of Economics did not hire its own newly minted PhDs, Merton said, so he hadn’t considered staying at MIT.

But MIT Sloan was not the economics department, so the rule did not apply.

“Things were going very well,” Merton recalled from his office at MIT Sloan more than four decades later. “I already had several published papers and more on the way. Why move from such a productive environment? I was perfectly comfortable, so I happily accepted the offer.”

Merton would eventually leave after 18 years, teaching at Harvard Business School before returning to MIT Sloan in 2010. But before that, while in his twenties, he worked with his MIT Sloan colleague Myron Scholes and independent consultant Fischer Black on a model for pricing stock options that had a dramatic impact on both financial theory and practice.

Black and Scholes developed a method for pricing options based on the Capital Asset Pricing Model. Merton then applied his continuous-time portfolio theory to show what their pricing model would produce as a consequence of ruling out arbitrage opportunities in the financial markets. This alternative approach showed that the option prices derived by Black and Scholes held up under considerably more robust assumptions than those in their original work.

The model that resulted, celebrating its 40th anniversary of its publication this year, came to be known as Black-Scholes, or Black-Scholes-Merton.

“They had the fundamental insight of undertaking a dynamic trading strategy in the underlying stock and the risk-free asset to hedge the systematic risk of an option position, and thereby create a portfolio of stock, risk-free asset, and option whose Capital Asset Pricing Model equilibrium expected return would equal the risk-free interest rate,” Merton said. “In addition to naming it the Black-Scholes model, my most significant contribution to the model was to show that if you go to shorter and shorter trading intervals, their same dynamic strategy rules will eliminate all the risk, which has the implication that you have a way to synthesize the option, even if the option doesn’t exist. By following a set of rules for trading the stock and the risk-free asset, I could create a portfolio that produced exactly the same payoff as the option.”

It soon became clear that the methodology could be applied to an array of securities’ pricing. Everything from convertible bonds to debt to warrants could be priced, hedged against, sold, and traded. The model would impact the pricing and risk assessment for instruments traded in the newly created national mortgage market and the student loan market, among others.

“Seldom has the marriage of theory and practice been so productive,” the financial historian Peter Bernstein wrote in *Capital Ideas: The Improbable Origins of Modern Wall Street*.

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*As Black-Scholes-Merton was being developed, Merton taught the method at MIT Sloan.*

“I started teaching in the fall of 1970. I taught the first-year finance course, and then I taught advanced capital markets. I put the general theory of how to price options and corporate liabilities—what came to be called ‘derivative securities’ generally—into the Master's classes.

“It wasn’t some special seminar or workshop. I actually taught it right in this mainstream second-level class beginning in 1970-71. The finance faculty—Stewart Myers, Myron Scholes, Gerry Pogue, and myself—were all junior and very young and it was kind of like leaving all the kids alone at home with no adult supervision. We simply did what we thought was best in research, teaching, and thesis supervision.

“I introduced the model into the classroom because I was convinced that this stuff was going to be very important for practice. And at that time there was no notion of continuing education. So I said 'In a way, it's more important that the Masters' students get this now than the PhD students. The latter will get it sooner or later as they study the scientific literature, but the former will never see it.' So I worked out a way to teach it to the students using nothing more than calculus and basic probability, which was at the time an entrance requirement for the Sloan Master’s program.

“The story is a good one because it worked out. If it hadn't worked out, I would have wasted their time. But the result was that there was a whole slew of Sloan graduates who had this material as Master's students before it was even published. And as it turned out, they were a pretty happy set of students after they left for practice because they had been let in on the foundation methodology, as 20-something-year-olds, for what turned out to be a 40-year revolution in the financial services industry.”

*Timing was everything.*

“Could we have predicted at the time how big this would get? No, of course not. Had we done this work in 1960-62, it would have probably gotten published and had no immediate impact on practice. But it was the 1970s. The stock market fell by 50 percent in real terms between mid-1973 and the end of 1974. Treasury interest rates were in double digits, peaking at over 20 percent in 1981. Inflation rates achieved levels not seen since the Civil War, with some price controls introduced and then abandoned. Suddenly the Bretton Woods agreement fixing global currencies was abandoned and world currencies started fluctuating for the first time in nearly 30 years. The first oil crisis occurred, with the price of oil going from $2.50 a barrel to $13. And all of this was happening in an environment of high unemployment. There was an explosion of new risks flowing throughout the system from everywhere.

“The response to that—perhaps the only functional aspect of a very dysfunctional disaster—was an explosion of financial innovation. There was so much need to manage these risks. Existing and new exchanges created a wide array of financial futures and option markets for efficient transfer and reallocation of the wide array of risks—equities, interest rates, currencies, commodities. In particular, the Chicago Board Options Exchange opened its doors in April of 1973, about the same time that our papers were finally published. The money market fund was invented and interest-bearing checking accounts came into being.

“We came up with this sort of universal model right at the right time as the financial world was exploding in innovation in response to a horrible set of economic financial conditions. These risk markets started to flourish and develop. The rapid, widespread adoption of the option pricing model in practice was driven out of need.

“So first we had the stock market, options, options and stock, right out of our paper. I applied it later in the 70s to valuing and describing the risks of loan guarantees and deposit insurance from the government. At the same time, a complete model for the pricing of credit risk came from that same structure.

“It's turned out that the same methodology is still the way it's done today, 40 years later. In a world that is innovating not only within markets, like the equity market, but across markets—the mortgage markets, the fixed income markets, currency—the point was that you had the confidence and knowledge that if someone came in to you and said 'We've created a new market, we need a new [financial device],’ well, most people would panic and say ‘I don't know how to do that.’ But those trained in the methodology said ‘We know how to do that.’

“It made possible an enormous amount of innovation across these markets, because it was a kind of universal methodology people could apply. It was a combination of what we did, and timing, and how the world evolved. For all of the stuff that's done involving derivatives, the basic replicating methodology is still today the one that's used. And, you know, that's actually been pretty cool.”

*In 1997, Merton almost missed the phone call informing him he was a winner of the Nobel Memorial Prize in Economic Sciences. He was 53 at the time, the second-youngest to ever receive the prize for economics. He shared the award with Scholes. Black passed away in 1995, but was mentioned by the Nobel committee.*

“I was in my place down the river from Sloan at the Esplanade, where I live. I was going out to get the first shuttle [to New York City] in the morning. If I had thought there was going to be, say, a one-in-twenty chance, wouldn’t I have just sort of waited around to see if the phone rang, and if it didn’t, leave?

“So I'm literally going out the door and the phone rings, and in an instant I said to myself ‘Should I answer it? Well, if I do, maybe I'll miss my plane. Well, if it's important maybe they will leave a message and I'll get it when I get to New York.’ So I say ‘Oh, I'll pick it up and say I'm running to a plane and so forth.’ So I pick it up and there's this deep voice that says ‘Professor Merton, my name is Dr. Bengt Samuelsson, I'm the chairman of the Nobel Foundation, and I have some interesting news for you.’ At which point he tells me that I had been chosen and then he put the head of the economics selection committee of the Swedish Royal Academy, Bertil Naslund, on the phone to congratulate me. I know why he did that, I think. Although we weren't personal friends or colleagues, I had met Bertil, so his congratulating me told me the phone call was for real.

“They were trying to find Myron, who was somewhere in California. He was off with his fiancée and they couldn't find him. He found out from his brother, who heard it on the radio.”

*Black-Scholes had an almost immediate impact on the burgeoning options market. In *Capital Markets*, Bernstein wrote that the number of call option contracts changing hands at the Chicago Board Options Exchange jumped from 911 on opening day in 1973 to more than 20,000 by mid-1974 to 100,000 in 1977. Merton credits the Nobel selection in part to the model’s real-world use.*

“Nobel had the idea that he wanted the work receiving the prize to have an impact on society. And everybody could see this work had a huge global impact on the financial systems, their operations and use. It was recognized that developing the new methodology had not only been a challenge intellectually, but had a material impact on practice. It's an example of something that basically came out of pure theory and evolved very rapidly into something in the mainstream of practice.

“By 1975, every single person on the floor of the [Chicago Board Options] exchange was using the Black-Scholes formula for pricing and determining the position mixes of options to hedge their risks. Texas Instruments created a specialized hand-held calculator. It had the formula, the hedge ratios, everything, in it. In no time at all, Black-Scholes went from theoretical to something that everyone used. Not because they were academically interested, but because it was a necessity. It was need that drove option traders on the floor of the CBOE to do that. It not only gave the price, but it also gave the risk. So all the guys on the floor knew ‘If I go long on this many of these options, and short on this many of those options, with this ratio, I'm balanced.’ Well, that was critical or they couldn't operate. Right from the beginning, that happened. In terms of speed of adoption and depth of adoption, I don't think there's anything quite comparable.”