物理学家到金融大师：Derman的量化人生自述

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"《我的量化人生》（My Life as a Quant）是高盛执行董事、哥伦比亚大学金工系主任埃曼纽尔·德曼撰写的一本自传性回忆录，记录了他的职业生涯转变，从物理学家到码农再到金融界的宽客。这本书不仅描绘了他在学术界与诺贝尔奖得主共事的纯理论环境，以及面对世俗成功压力时的内心挣扎，还深入探讨了他如何将物理学思维带入投资银行领域的过程。在书中，德曼以一种诚实而深刻的方式，分享了他从物理学研究的世界步入金融市场的经历。他揭示了学术界追求纯粹知识的激励机制，以及这种转变过程中所面临的矛盾情绪，即在追求理论深度的同时，必须面对现实世界中盈利与损失（Profit & Loss, P&L）的残酷法则。德曼的个人叙述为读者提供了一扇窗口，让他们窥见物理学、金融和量化金融（PhyNance）这三个领域之间的交叉融合，以及它们在现代金融市场中的实际运作。该书获得了广泛赞誉，如数学家、作家及基金经理保罗·威尔莫特的评价，他认为这是一本关于一个时代中杰出人物历程的真实记录，对于想要成为量化分析师的人士、金融历史学者以及对学术界和业界运作机制感兴趣的门外汉来说，这本书是必读之作。另一名评论者彼得·C也高度评价了德曼作为这一代领军人物的洞察力，他通过引人入胜的故事，展现了不同文化背景下的物理学、金融世界，以及二者如何交织创造出量化金融这一强大的融合体。通过《我的量化人生》，读者不仅可以了解到一个专业人士的职业发展路径，还可以反思学术与商业的界限，理解理论与实践如何相互作用，以及如何在追求知识与市场利润之间找到平衡。这本书不仅是一本金融专业书籍，更是一部关于人生的哲学思考，对读者有着深刻的启发作用。"

ously skilled mathematicians, modelers,and computer programmers who

prided themselves on their ability to adapt to new fields and put their

knowledge into practice. Wall Street began to beckon to them. In the

1980s, so many physicists flocked to investment banks that one head-

hunter I know referred to them as “POWs”—physicists on Wall Street.

THE MOST SUCCESSFUL THEORY

What is it that physicists do on Wall Street? Mostly, they build models

to determine the value of securities. Buried in investment banks, at

hedge funds, or at financial software companies such as Bloomberg or

SunGard, they tinker with old models and develop new ones. And by

far the most famous and ubiquitous model in the entire financial world

is the Black-Scholes options pricing model. Steve Ross, a famous finan-

cial economist, options theorist, and now a chaired professor at MIT,

wrote in the Palgrave Dictionary of Economics that “.. . options pricing

theory is the most successful theory not only in finance, but in all of

economics.”

The Black-Scholes model allows us to determine the fair value of a

stock option. Stocks are commonplace securities, bought and sold daily,

but a call option on a stock is much more arcane. If you own a one-year

call option on IBM, for example, you have the right to buy one share

of IBM one year from today at a predetermined price: say, $100. The

value of the option on that future date when it expires will depend on

the prevailing value of a share of IBM. If, for example, a share sells for

$105 on that day, the option will be worth exactly $5; if a share sells

for less than $100, the option will be worth nothing. In a sense, the

option is a bet that the stock price will rise.

An option is a special case of a more general derivative security,a

contract whose value is derived from the value of some other simpler

underlying security on which it “rests.” A derivative security’s payoff at

expiration is specified in a contract via a mathematical formula that

relates the payoff to the future value of the underlying security. The

formula can be simple, as is the case with the stock option just

described, whose payoff is the amount by which the final stock price

exceeds the value of $100, or it can be extremely complicated, with a

payoff that depends on the prices of several underlying securities

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through detailed mathematical expressions. During the past twenty

years derivative securities have become widely used in the trading of

currencies, commodities, bonds, stocks, mortagages, credit, and power.

Derivatives are more intricate than unvarnished stocks or bonds.

Then why do they exist? Because derivatives allow clients such as

investment banks, money managers, corporations, investors, and specu-

lators to tailor and fine-tune the risk they want to assume or avoid. An

investor who simply buys a share of IBM takes on all the risk of own-

ing it; its value waxes and wanes in direct proportion to IBM’s share

price. In contrast, an IBM call option provides potentially unlimited

gain (as the share price rises above $100) but only limited loss (you lose

nothing but the cost of the option as the stock price drops below $100).

This asymmetry between upside gain and downside loss is the defining

characteristic of derivatives.

You can buy or sell options retail on specialized options exchanges,

or you can trade them with wholesalers, that is, the dealers. Options

dealers “make markets” in options; they accomodate clients by buying

options from those who want to sell them and selling options to those

who

want to acquire them. How, then, do dealers handle the risk they are

forced to assume?

Dealers are analogous to insurance companies, who are also in the

business of managing risk. Just as Allstate must allow for the possibility

that your house will burn down after they sell you an insurance con-

tract, so an options dealer must take a chance of a rise in IBM’s stock

price when he or she sells you a call option on IBM. Neither Allstate

nor the options dealer wants to go broke if the insured-against scenario

comes to pass. Because neither Allstate nor the dealer can foretell the

future, they both charge a premium for taking on the risks that their

clients want to avoid.

Allstate’s risk strategy is to charge each client a premium such that the

total sum they receive exceeds the estimated claims they will be obliged

to pay for future conflagrations. An option dealer’s risk strategy is dif-

ferent. In an ideal world, he or she would simply offset the risk that

IBM’s price will rise by buying an IBM option similar to the one he or

she sold, from someone else and at a cheaper price, thereby making a

profit. Unfortunately, this is rarely possible. So instead, the dealer manu-

factures a similar option.This is where the Black-Scholes model enters

the picture.

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The Black-Scholes model tells us, almost miraculously, how to man

acture an option out of the underlying stock and provides an estimate of

how much it costs us to do so. According to Black and Scholes,mak-

ing

options is a lot like making fruit salad, and stock is a little like fruit.

Suppose you want to sell a simple fruit salad of apples and oranges.

What should you charge for a one-pound can? Rationally, you should

look at the market price of the raw fruit and the cost of canning and

distribution, and then figure out the total cost of manufacturing the

hybrid mixture from its simpler ingredients.

In 1973, Black and Scholes showed that you can manufacture an IBM

option by mixing together some shares of IBM stock and cash, much as

you can create the fruit salad by mixing together apples and oranges.

Of course, options synthesis is somewhat more complex than making

fruit salad, otherwise someone would have discovered it earlier.Whereas

a fruit salad’s proportions stay fixed over time (50 percent oranges and 50

percent apples, for example), an option’s proportions must continually

change. Options require constant adjustments to the amount of stock and

cash in the mixture as the stock price changes. In fruit salad terms, you

might start with 50 percent apples and 50 percent oranges, and then,

as apples increase in price, move to 40 percent apples and 60 percent

oranges; a similar decrease in the price of apples might dictate a move to

70 percent apples and 30 percent oranges. In a sense, you are always try-

ing to keep the price of the mixture constant as the ingredients’ prices

change and time passes.The exact recipe you need to follow is generated

by the Black-Scholes equation. Its solution, the Black-Scholes formula,

tells you the cost of following the recipe. Before Black and Scholes, no

one even guessed that you could manufacture an option out of simpler

ingredients, and so there was no way to figure out its fair price.

This discovery revolutionized modern finance. With their insight,

Black and Scholes made formerly gourmet options into standard fare.

Dealers could now manufacture and sell options on all sorts of under-

lying securities, creating the precise riskiness clients wanted without

taking on the risk themselves. It was as though, in a thirsty world filled

with hydrogen and oxygen, someone had finally figured out how to

synthesize H

Dealers use the Black-Scholes model to manufacture (or synthesize,

or financially engineer) the options they sell to their clients.They con-

struct the option from shares of raw stock they buy in the market.

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Conversely, they can deconstruct an option someone sells to them by

converting it back into shares of raw stock that they then sell to the

market. In this way, dealers mitigate their risk. (Since the Black-Scholes

model is only a model, and since no model in finance is 100 percent

correct, it is impossible for them to entirely cancel their risk.) Dealers

charge a fee (the option premium) for this construction and decon-

struction, just as chefs at fancy restaurants charge you not only for the

raw ingredients but also for the recipes and skills they use, or as cou-

turiers bill you for the materials and talents they employ in creating

haute couture dresses.

LIFE AS A QUANT

The history of quants on Wall Street is the history of the ways in which

practitioners and academics have refined and extended the Black-

Scholes model. The last thirty years have seen it applied not just to

stock options but to options on just about anything you can think of,

from Treasury bonds and foreign exchange to the weather. Behind all

these extensions is the same original insight: It is possible to tailor secu-

rities with the precise risk desired out of a mix of simpler ingredients

using a recipe that specifies how to continually readjust their propor-

tions.The readjustment depends on the exact way in which the ingredi-

ents’ prices move.

Because bond prices don’t move exactly like stock prices, the recipe

for a bond option must differ from that of the classic Black-Scholes

model. But this is a subtlety—when a new product is first created,

a crude Black-Scholes-like model often suffices. Then, an arms race

begins.

As competitive pressures increase and spreads tighten, quants

at different firms refine and extend their first pass at the model, add-

ing new and more accurate descriptions of the motion of the ingredi-

ents and obtaining better recipes for the salad. Extending the model

demands a grasp of financial theory, mathematics, and computing, and

quants work at the intersection of these three disciplines.

The life of a practitioner quant in a trading business is quite different

from that of a physicist.When, after years of physics research, I first came

to work on Wall Street at the end of 1985, my new boss asked me to

take a second pass at a problematic Black-Scholes-like model for bond

options that he had built a year earlier. I started out slowly and carefully,

working like a physicist; I read the relevant papers, learned the theory,

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diagnosed the problem, and began to rewrite the computer program

that made the model work. After several weeks he became impatient

with my lack of progress.“You know,” he said a little sharply as he took

me aside, “in this job you really need to know only four things: addi-

tion, subtraction, multiplication, and division—and most of the time

you can get by without division!”

I took his point. Of course, the model used more advanced mathe-

matics than arithmetic. Yet his insight was correct. The majority of

options dealers make their living by manufacturing the products their

clients need as efficiently as they can—that is, by providing service for

a fee. For them, a simple, easy-to-understand model is more useful than a

better, complicated one.Too much preoccupation with details that you

cannot get right can be a hindrance when you have a large profit mar-

gin and you want to complete as many deals as possible. And often, it’s

hard to define exactly what constitutes a “better” model—controlled

experiments in markets are rare.Though I did ultimately improve the

model, the traders benefited most from the friendly user interface I pro-

grammed into it.This simple ergonomic change had a far greater impact

on their business than the removal of minor inconsistencies; now they

could handle many more client requests for business.

Although options theory originated in the world of stocks, it is

exploited more widely in the fixed-income universe. Stocks (at least at

first glance) lack mathematical detail—if you own a share of stock you

are guaranteed nothing; all you really know is that its price may go up

or down. In contrast, fixed-income securities such as bonds are ornate

mechanisms that promise to spin off future periodic payments of inter-

est and a final return of principal.This specification of detail makes fixed

income a much more numerate business than equities, and one much

more amenable to mathematical analysis. Every fixed-income security—

bonds, mortgages, convertible bonds, and swaps, to name only a few—

has

a value that it depends on, and is therefore conveniently viewed as a

derivative of the market’s underlying interest rates. Interest-rate deriv-

atives are naturally attractive products for corporations who, as part of

their normal business,must borrow money by issuing bonds whose value

changes when interest or exchange rates fluctuate. It is much more chal-

lenging to create realistic models of the movement of interest rates,

which change in more complex ways than stock prices;interest-rate mod-

eling has thus been the mother of invention in the theory of derivatives

for the past twenty years. It is an area in which quants are ubiquitous.

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