My Life as a Quant (24 page)

From the moment it appeared in print, the Black-Scholes-Merton theory was embraced, not only by academics but by options dealers. Before the advent of the model, a dealer who sold a call option to a client had to take the other side of the trade; the dealer then bore the risk, if the stock price went up, of having to pay the client out of pocket. After the model's dawn, a dealer could use its recipe to roll his or her own option out of stock and cash, and estimate the cost of doing so. The dealer could then sell the homemade option to the client, ideally being left with no risk at all.

Options dealers soon began to use the Black-Scholes model to manufacture options out of raw stock and then sell them. Dealers charged a fee for this manufacture, just like any other value-added reseller.

On Wall Street, quants, traders, and salespeople make daily use of the stock options model and its extensions. During the past thirty years, academics in business schools, mathematicians in math departments, and quants in investment banks and hedge funds have applied similar methods to produce models for options on bonds, options on interest rates, options on credit ratings, options on energy, and even options on volatility itself. Though the simple and profound idea of Black, Scholes, and Merton has remained unchanged, the mathematics has become more elaborate, complex, and daunting.

Black and Scholes's original model assumed almost platonically simple markets. They allowed for the uncertainty of future stock price movements, but ignored other more detailed complexities. However, their model proved to be extensible and robust—one could augment it to take account of the imperfections of actual trading. The model accommodated these and other refinements while leaving the basic strategy substantially unchanged. Options theory is one of the great triumphs of economics, conceptually simple and pragmatically useful despite its complex mathematics. If only the rest of economics had similar efficacy!

I knocked on the door of Fischer's office and entered. Inside, it was quiet and low-lit, a location for work rather than meetings. At Goldman an office was a token of seniority, a very expensive pocket of personal real estate. Many of the fancily furnished offices on the equity floor were largely uninhabited, filled with tombstones of past deals executed by the traders and salespeople who had no time for office work. Fischer's office was much less glamorous; it was dominated by a large Nike poster of a long road disappearing into the distance and, below it, the caption: “The race is not always to the swift, but to those who keep on running.”

Brought to Goldman Sachs from MIT by Bob Rubin in 1984, Fischer was one of the first finance academics to head for Wall Street; he became a Goldman partner in 1986. Unlike other professors in the industry who maintained their umbilical links to the safe haven of academia, Fischer embraced the business world wholeheartedly. Now I was about to meet him.

After a brief introduction, I began to show him
Bosco
, the bond options model and its graphical user interface I had built for the options desk. Fischer, like everyone else in the less numerate Equities Division, used a PC running DOS, but I had developed my software on the more advanced VAX we all used in Fixed Income. I logged on to the VAX through a VT-100 terminal emulator on Fischer's PC. Almost as soon as my program started running the VAX itself crashed, and we were left looking at the frozen screen image of my calculator. I couldn't run the program, I couldn't toggle or change the values of any of the fields—we could only observe them carefully on the monitor. I offered to come back later when the VAX was up again, but Fischer was quite unperturbed. He spent the next hour carefully examining the screen I had built, commenting on its layout.

Those were the days of limited computer-screen real estate: I had 24 lines of 80 characters to work with, and all of the approximately twenty-five input and output fields used in
Bosco
had to fit in that space. Fischer meticulously inspected each field, making reasonable but almost picayune comments about some of their labels. Because of the lack of space, I had had to abbreviate most labels, and had half-jokingly contracted the variable named
bond duration
to the inelegant
durn
, which he particularly disliked. Later in the conversation—because I was unschooled in finance and had been in the field only a few months—I periodically referred to “an option on a future contract” and each time Fischer quickly corrected me by brusquely interjecting “
futures
contract.”

I was surprised at his willingness to spend so much time on the mere interface to Ravi's model, when he hadn't yet seen the calculator work or listened to my explanation of how I had modified it. When I returned to my fixed-income colleagues later that day, my feelings a little bruised by his criticisms, I scoffed at his attitude. But I soon discovered that Fischer was always a stickler for precision, and clear expression was an invariant devotion of his. Over the years, I became a convert and tried as hard as I could, in anything I subsequently wrote, to be as clear and didactic as possible.

During the weeks after he first examined my frozen
Bosco
computer screen, I learned much more about Fischer's computer prejudices. Some of them were quite reactionary. He disapproved of “mice” and other computer pointing devices. He thought keyboards were the ideal means of data entry; he insisted that anything one could do with a mouse could be done better with macro redefinitions of particular keys on the keyboard. Finally, he disliked graphics, and claimed that unadorned tables of numbers were more evocative and revealing. There was no persuading him on these issues; they were a part of his near-magnificent obsession about presentation style.

There were other quirks, harmless but irritating. He demanded strict standards on the display of numbers, intensely objecting to any printout that included more digits after the decimal point than was warranted by the accuracy of the calculation. Now everyone agrees that it is objectionable to report a measurement of room temperature as 73.1457° F—the implied precision is false—but Fischer logically extended his disapproval to the display of any excess zeros at the end of a decimal number, a feature he dubbed “trailing zeros.” If a bond had a yield of 12 percent, he wanted it printed as a confident “12%” rather than as a tentative “12.00%” which would have suggested that it was only accurate to two decimal places. If Fischer did not find the display satisfactory, you could spend too much time talking to him about style and never progress to the content.

Eventually, therefore, everyone who worked with Fischer for even a little while wrote their own version of a subroutine that stripped all the trailing zeros off a number before displaying it. Bill Toy and I used to joke that you could identify Fischer's collaborators by searching their hard disks for a subroutine called
removeTrailingZeros
( ).

Sometimes Fischer took this a little too far. One day a few months later I made use of an options calculator built by someone in his group. It required that you enter the stock's dividend yield, and so I entered the number “0” in the field. For a brief subliminal instant I saw the numeral zero I had entered fluoresce onto the screen, and then vanish, leaving an empty field. Thinking I had made a typing mistake, I entered the zero again. Again, miragelike, the ghostly zero flickered and deliquesced. Then I realized what was happening. The programmer had blindly followed Fischer's dictum to remove all trailing zeros, and since the number “0” was all zeros, it removed the entire number, leaving the impression that nothing had been entered. The program had no respect for the philosophical distinction between nothing and zero.

Just as on the first day I visited him, Fischer was always quiet and calm, always in visible equilibrium. He never seemed to allow his work life to become an exercise in the exhausting multitasking (and the macho pride in coping with it) that quickly became a way of life for people at investment banks. Most often, when you went to visit him, you would find him reading, or on the telephone, or sitting with his back to the door, his PC keyboard on his lap and his chair swiveled 180 degrees to face the PC on the bureau by the window behind his chair, entering notes into Thinktank, a late-1980s organizer program he used constantly.

Fischer filed all his memos and notes in Thinktank; Beverly Bell, his editor at Goldman, said that he accumulated over 20 million bytes of text in it, from addresses and phone numbers to thoughts and ideas. People I knew in his group claimed that he conducted a continuing and eager correspondence with the Thinktank designers in order to suggest additions or modifications he wanted to see.

Fischer was precise and organized, quite punctilious. Every day he ordered the same ascetically healthy meal delivered to his desk. He liked to wear a Casio information-storing watch, which prompted some of his employee-admirers to do likewise. In his office giving audience, if you said something he found useful, he wrote it down with his fine-pointed mechanical pencil on a fresh sheet of his ruled white pad, and then tore it off and inserted it into a new manila folder which he labeled and then placed in one of his file drawers. In an article published after his death, Beverly described the 6,000 files he left behind, now archived at MIT.

Fischer was unashamed of his nerdish enthusiasm for technology, in contrast to most of Wall Street in the 1980s, where important managers prided themselves on their ignorance of computers. Some managers I knew eschewed not only computers, but even desks in their offices, preferring a large conference table to signify their major role as decision makers.

When I began to work with Fischer, I thought he had some strange tastes. You couldn't easily guess his attitude to one question by knowing his opinion about another, though what he said was always thoughtful and sensible. But over subsequent years I learned that he was a rarity, one of those people you only occasionally meet, someone whose character is a coherent whole even though its parts seem uncorrelated. At bottom, he simply liked to think through everything for himself. This didn't make him a great rebel, but rather an outsider whose work had vast impact on the world of insiders. It was impressive to watch.

Back in FSG after meeting Fischer, I continued studying the classic Black-Scholes model for stock options and the way in which Ravi had modified it for use on the bond options desk.

Options have value because future stock prices are uncertain, and the further out into the future you go, the more uncertain they become. A great deal of options theory is concerned with the modeling of future uncertainty.
Figure 10.1
illustrates in a simplified way how Black and Scholes pictured the uncertainty of a stock's future price. As time passes, the region in which the future stock price is likely to lie progressively widens. A stock worth $100 today could be worth anything between zero and a very large number thirty years from now. (If you bought internet stocks in the late 1990s, you understand this all too well.)

Figure 10.1
The distribution of possible future prices over 30 years for a stock whose price is $100 today. The more time passes, the greater the uncertainty in the future price. The darker the shading, the more likely the price will be in that region.

Bonds are different. While no one knows the future price of a stock, a $100 initial investment in a thirty-year Treasury bond is guaranteed to pay you back exactly $100 when the bond matures. The shaded region in
Figure 10.2
illustrates the approximate range of a bond's future price: It widens as we move away from the known bond price of $100 today, and then converges towards the certain value of $100 thirty years from now.

Figure 10.2
The distribution of possible future prices for a bond whose price is $100 today. After thirty years, the bond must again be worth exactly $100. The darker the shading, the more likely the price will be in that region.

The straightforward but simplistic way to value bond options in 1985 was to use the Black-Scholes model as is, thereby implicitly assuming that bond prices followed the distribution of
Figure 10.1
rather than
Figure 10.2
. For short-term options expiring within a year or two, it didn't matter much. You can see that, for the first year, the distribution of bond prices closely resembles the distribution of stock prices. Consequently, the Black-Scholes model is not a bad approximation for short-term (one-year) bond options. But for longer-term options, the bond and stock distributions are vastly different. For long-term bond options, a different model is needed.