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Unformatted text preview: TAX ' REGULATION  FINANCE % APRlL 2005
VOL 5, NO 8 WG
613 ' FINANCIAL PRODUCTS REPORT DERIVATIVES AND THE DEMAND FOR FINANCIAL
MATH—IT IS ROCKET SCIENCE NIELS NYGAARD THE TRENDS POINT TO ONE UNDE
NIABLE TRUTH: IN THE FUTURE,
FINANCIAL MATHEMATICS GRADU
ATES WILL BE IN DEMAND. n MIT physics pro—
fessor recently noted that the most remarkable
change he has witnessed
during the past four
decades is the number of
physics and math majors
going into the field of
finance. “Even ten years
ago you just didn’t see
this,” he said, adding that,
“never in my wildest
dreams would I have pre~
dicted this.” While an exact expla—
nation for the change is
difficult to provide, two
key trends may be rele—
vant. The first is the exploi
sion in the growth of the
derivative markets during
the 19905, and the other
is the availability ofa new
kind of education espe cially suited to under—
graduates with excellent
training in mathematical
and computational skills:
the Masters Degree in
Financial Mathematics.
In the fall of 1996, 25
math, physics, and com—
puter science graduates
entered the inaugural
class of the University of
Chicago’s Master of Sci—
ence in Mathematical
Finance Program, The one—
year program, whose con—
tent and curriculum were
scrupulously researched in
collaboration with several
industry experts, was
intended to train students
in the methods of mathe—
matics as they are applied
to finance. The program as
it was in 1996 was approx
imately one—half mathe—
matics courses, such as
stochastic calculus, partial
differential equations, and
optimization theory, and one—half finance, inclucL
ing courses in derivative
markets and instruments
as well as heavily theoe
retical courses in the
mathematics of deriva—
tives pricing. At the time,
almost no programs of this
kind existed, and it was
questionable whether
Chicago’s new program
made it one too many. it was not that high
powered mathematics
was not already an impors
tant part of the world of
finance. Rather, high—
powered financial maths
ematics was the province
of “rocket scientists,” that
is, math, physics, and
engineering PhDs with
research training in math
ematical and physical sci—
The issue was
whether the industry had
any use for Masters stu
dents and whether they
could compete with the EHCES. Reprinted with permission Warren, ﬁnrham 8. Lamont of BIA myriad newly minted PhDs who
were regularly finding their way to
Wall Street. When the University of
Chicago started to research its Math—
ematics of Finance Program in 1994,
much of the feedback that the
school received was along the lines
of “great program, I don‘t know if
your students are going to get jobs." Today, eight years later, the Inter
national Association of Financial
Engineers lists over 70 Masters in
Financial Mathematics programs on
its website, anci the number of such
programs has been growing at an
astounding rate.IL Many of the
world’s top universities now offer
financial mathematics programs.
Besides the University of Chicago,
these include Princeton, Stanford,
MIT, Columbia, Cambridge. and
Oxford. Each year the International
Association of Financial Engineers
holds its National Financial Mathe
matics Career Fair in New York City
and financial giants such as Golds
man Sachs, Citigroup, and Merrill
Lynch regularly attend this meeting
to recruit graduates from 20 differ—
ent math Finance programs.2 At its core, the programs’ popu
larity and growing importance can
be explained quite simply by the
incredible anti surprising usefulness
of mathematics in finance, espe
cially in financial derivatives. While
this area became an important part
of the financial landscape in the
19705. it truly came into its own du r—
ing the 1990s. In March 1999, Alan Greenspan,
Chairman of the Federal Reserve
Board, speaking before the Futures
Industry Association, opened with
this statement: “By far the most sig
nificant event in finance during the 1 See www.late.0rg/?id=academicprngramsi 2 For more information, see www.iate.org/
events.php?event_id=349?2567. pasr decade has been the extram—
dinary development and expansion
of financial derivatives." He credits
derivatives for their unique ability
to break up risk into component
parts and trade them with counter
parties more willing and able to take
on those risks. As he noted: This unbundling improves the
ability of the market to engen
der a set of product and asset
prices far more calibrated to the
value preferences of consumers
than was possible before deriv—
ative markets were developed.
The product and asset price sig—
nals enable entrepreneurs to
finely allocate real capital facili
ties to produce those goods and
services most valued by con—
sumers, a process that has
undoubtedly improved national
productivity growth and stan
dards of living. What Greenspan did not say is
that the tremendous growth, which
has continued at the same rate into
this decade, has created tremen
dous demand for highly trained indi—
viduals capable of understanding
and improving the underlying the—
oretical models for pricing and
hedging the derivative instruments.
This is because, when it comes to
the pricing, hedging, and risk man
agement of financial derivatives,
sophisticated mathematics is not
optional; it is required reading. The
creation of new products, their
design, and implementation—from
the creation of risk systems to hedg
ing schemes to research pieces that
educate clients—requires exactly
the kind of knowledge and back
ground that financial mathematics
graduates have. And this knowl—
edge is not easy to come by, even
for math and physics PhDs. Hence APRIL 2005 the need for highly specialized train—
ing in financial mathematics. With this, one might think that
financial mathematics programs are
merely professional schools for
wouldbe, wantto—bc derivatives
traders and sales people. in fact, the
ambitions of financial mathematics
programs extend beyond deriva—
tives to the broader world of finance,
where another exciting develop
ment in finance during the past
decade comes into play. Enter quan
titative investment strategies. A major investment bank recently
posted the following job description
under the heading “Quantitative
Trading and Research": As products in the financial mar—
kets become more sophisticated
and proprietary trading risks
increase, the successful integra
tion ofquantitative methods with
trading takes on a greater sig
nificance. Quantitative traders
are primarily focused on pro
viding capital and managing risk
on customer trading desks such
as Mortgages, Fixed Income,
Equity, Foreign Exchange (FX),
and Credit Derivatives. The rise
in prominence of proprietary
trading also has led to the devel
opment of increasingly sophisti—
cated trading techniques
designed to identify market inef—
ficiencies in Statistical Equity
Arbitrage, Fixed income Arbi—
trage, and Municipal Arbitrage. Trading strategies based on quan—
titative techniques are not new to
Wall Street. indeed, it is widely
knorvn that David Shaw, founder of
the hedge fund giant D.E. Shaw,
worked in a highly quantitative trad—
ing group in the mid—to—late 19805
before leaving to start his own fund.
What is new, however, is the explo— sive growth of hedge funds and
trading groups within investment
banks that specialize in deploying
capital using sophisticated statisti~
cal analysis. What has made this possible is
the rapid decline in both the cost of
computing power and storage. Both
components are necessary to
manipulate the vast amounts of data
available today. A typical quantita
tively driven hedge fund can easily
possess multiple “terabytes" of data
on global markets. The ability to
store and rapidly retrieve such large
amounts of data requires comput
ers with large amounts of oneboard
RAM, fast processors, and lots and
lots of disk space. What does one do with all this
computing power and data? Two
words: analyze it. FINANCIAL MATHEMATICS
Financial mathematics spans several
subject areas crossing various dis—
ciplines. To be truly effective, stu
dents must learn everything from the
mathematics related to partial dif—
ferential equations, stochastic
processes, and optimization to
econometrics, data analysis, and
numerical analysis at the same time
they are mastering the intricacies of
the uses of financial derivatives
across several different markets. The
mathematics in financial math is
essential to understanding the pric
ing models that assign fair values to
financial derivatives. Equally important to the theory
is the ability to implement the mod—
els into practical applications for
analyzing the profitability and risk
of particular derivative transactions
and portfolios of derivatives. These
practical applications make the
models accessible to traders and
sales people who need to commuw
nicate the outputs of such models.
in this regard, most financial math— JOL ‘9 NC ’3 ematics programs emphasize corn—
puter implementation of financial
models in languages like C++ and
java. Alongside the mathematical the
ory and computer implementation
of ﬁnancial mathematics, programs
also require courses in financial
markets, financial instruments, and
their uses in the “real world“ to train
students in the practical workings
of global markets and the instru—
ments that trade on them. They
bridge theory with practice by
explaining the mechanics of trad
ing and the uses for the products,
expanding, if you will, on
Greenspan’s remarks above. The
best financial mathematics programs
are able to leverage their reputations
to attract world—class practitioners to
participate in the teaching of courses
to give students a real—world look
at the use of such instruments. WHAT l5 NEW l5 THE EXPLOSii/E GROWTH OE HEDGE FUNDS AND
TRADING GROUPS WiTHI'N
lNVESTMENT BANKS THAT
SPEClALlZE lN DEPLOYING CAPlTAL USlN
SOPHlSTlCATED STATlSTlCA
ANALYSIS. FINANCIAL DERIVATIVES Derivatives are financial instruments
whose value and payouts depend
on the movement ofother financial
variables. This simple statement
belies both the usefulness and com
plexity of derivatives. But consid—
ering that until the mathematical
sophistication of the instruments
was first truly understood—studied
in the seminal work ofFischer Black,
Myron S. Scholes, and Robert C.
Merton in 1972 for which Scholes
and Merton later (1997) won the
Nobel prize—derivatives were lit— erally nothing more than a back—
water business of little significance
to the ﬁnancial world. This changed in the early 19705.
First, Black, Scholes, and Merton
published their work on option pric—
ing theory3 and demonstrated that
the value of a call option on a corn—
pany’s stock is determined by the
solution to a certain partial differ
ential equation. Second, the Chicago
Board Options Exchange opened its
doors. To understand the impor—
tance of Black, Scholes, and Mer
ton, all one has to do know is that,
within six menths of the options
exchanges opening, Texas Instru
ments was offering a hand—held cal—
culator with the Black—Scholes
formula programmed into it. It is indisputable that, from the
early 19703 to today, derivative
instruments have been one of the
most successful new products in any
industry since the invention of the
automobile. From essentially zero
sales in 1970, derivatives have
grown to be a multi—trillion dollar
industry and are still sustaining dou—
ble—digit growth 30 years later. What
drives this growth is their funda
mental importance to endusers—
hedge funds, commercial banks,
corporate treasuries, and central
banks—in hedging financial risks.
The ability for any of these to hedge
such risks expands their fundamene
tal ability to operate their businesses.
Markets for these instruments allow
not onlyr for better management of
risks—that is, the hedging of risks
that were previously unhedgeable—
but for the measurement of risks that
were previously immeasurable. The
dual ability to measure and manage
financial risk is of unparalleled
importance in financial markets. Derivatives come in a variety of
sizes and shapes, but one way to
categorize them is along asset class
lines. There are interest rate deriv atives (e.g., an interest rate swap
may pay a customer according to
the current level of shortterm inter
est rates and be used to hedge risks
in a shifting interest rate environ
ment'), and there are equity deriva—
tives (eg, a put option might pay
a customer according to the value
of the S&P 500 index and be used
to hedge market risk exposure).
There are also foreign exchange
derivatives (e.g., foreign exchange
options), which pay off according
to underlying moves in FX markets. Finally, newer but perhaps most
important, are credit derivatives. A
credit default swaps pays a cus—
tomer in the event of a certain credit
defaulting. All of these instruments
play an increasingly important role
in the financial marketplace as
banks offer an increasingly compli
cated variety of such instruments to
a widening customer base, Sum—
marizing all of this, Alan Greenspan
recently remarked: No discussion of better risk man—
agement would be complete
without mentioning derivatives
and technologies that
spawned them and so many the other changes in banking and
finance, Derivatives have per7
mitted financial risks to be
unbundled in ways that have
facilitated both their measure
ment and their management.
Because risks can he unbun 3 Btack and Scholes, "The Pricing of Options and
Corporate Liabilities." 81 Journai of Potitical
Economy 637 (19T3). Merton, "Theory of
Rational Option Pricing,” 4 Journal of
Economics and Management Scrence 141
HE’S]. *1 ”Banking.” remarks by Chairman Alan Green
span at the American Bankers Association
Annuai Convention. New York, New York.
October 5, 2004 [http:/fwwfederaireserve.
gov/hoarddocs/speeches/ZOO4/20041005/
defaultJ'ltm}. 5 See Bank for International Settlements.
“Triennial Central Bank Survey of Foreign
Exchange and Derivative Markets Activity in
April of 2004." at http://www.iaisnrg/publr
rpfxOipdf. dled, individual financial instru—
ments can now be analyzed in
terms of their common underly—
ing risk factors, and risks can be
managed on a portfolio basis.
Concentrations of risk are more
readily identified, and when such
concentrations exceed the risk
appetites of intermediaries,
derivatives and other credit and
interest rate risk instruments can
be employed to transfer the
underlying risks to other entities.
As a result, not only have indi—
institutions
become less vulnerable to shocks
from underlying risk factors, but
also the financial system as a
become vidual financial whole has more resilient.‘ The growth of derivatives was
tremendous during the 19905 but
has continued unabated in the let
century. The BIS (Bank for Inter
national Settlements) tracks OTC
derivative markets in a once—every—
three—years survey of derivatives
dealers globally. From 1995 to 2004.
the daily turnover in interest rate
derivatives grew steadily from $151
billion to $1.025 trillion, represent
ing an annual rate of increase of over
21%.5 This is startling, especially
since interest rate derivatives were
already considered a mature indus
try. Similar huge growth occurred
in foreign exchange, equity, and
credit derivatives as well. Derivatives markets are com—
posed of a variety of players but cen—
tral to it are the derivatives
dealersithal is, investment banks
whose traders stand ready to buy
or sell in a variety of instruments.
These banks, such as Goldman
Sachs, Morgan Stanley, UB8, and
Credit Suisse First Boston, are usu—
ally organized along asset class lines
with the derivatives traders situated
physically close to the traders in the
underlying instruments of the asset AP RIL 2005 classes. 80, for example, an equity
derivatives trader sits on the equity
trading floor near the block traders,
program traders, and Nasdaq mar—
ket makers. The derivatives desk
consists of traders, sales people,
and a quantitative team. Traders
make the markets—they say at what
price they will buy and where they
will sell a certain instrument on a
certain day, at a certain time. Sales
people keep in close contact with
their customers and take requests
for pricing information on deriva—
tives as well as pitching trade ideas.
When a customer wants to do a
trade, he communicates the request
to the sales person who then asks
the trader to provide a two—way
market—a price at which he will buy
and a price at which he will sell.
From here, after a bit of routine dis—
cussion, a trade is executed. WiTHiN SiX MONTHS O
THE OPENING OF THE
CHiCAGO BOARD OPTlONS
EXCHANGE, TEXAS
iNSTRUMENTS WAS
OFFERiNG A HAND«HELD CALCULATOR WlTH TH
BLACK—SCHOLES FORMULA
PROGRAMMED iNTO i . All of this involves a tremendous
amount of mathematical, financial,
and technological sophistication.
Many of the instruments that a deriv—
atives desk offers are OTC deriva—
tives, meaning that a trade is a
private contractual arrangement
between a customer and a trading
desk. It involves an obligation by
both parties to pay certain cashflows
in the event of certain price move
ments. For example, in an equity
option, the bank may agree to pay
the counterparty if the price of the
underlying instrument (e.g., the S&P
500) falls below a certain level. The
bank, naturally. does not want to play the role of casino but instead
wants to individually hedge each
trade to ensure that each and every
trade turns a profit. This is where
financial mathematics plays its
biggest role. it was precisely the work of
Black, Scholes, and Merton that
demonstrated that not only does a
precise mathematical relationship
exist between the value of a deriv—
ative instrument and the underlying
economic variables that inﬂuence its
price, but also that there is a pre
cise way of hedging a derivative
transaction. Thus, if the formula
states that a certain option is worth
$1. a trader can sell the instrument
for$1.10, hedge it, and book a $0.10
profit. The mathematics behind this
are based on a financial notion
called “arbitrage—free pricing,"
which essentially says that the law
of one price must always hold. It
recognizes that two financially
equivalent bundles of goods, no
matter how differently they are bun—
dled, must have the same price.
From this simple observation and
some sophisticated mathematics, a
hedging scheme for stock options
came about, and every new deriv
atives pricing scheme since has been
based on this idea. To provide a twoway market on
a derivative instrument, a trader
must compute the fair price of the
derivative and undersrand the hedg
ing scheme that allows the realiza
tion of that price. The pricing
formulas must therefore be embeds
ded in technology that exposes to
the trader live market prices and
pricing models for a variety of deriv—
ative instruments. The trader must
also be able to confer with a quan
titative specialist to help interpret
the validity of the prices and hedges
in various market situations. After
all, the aim of the trader is to offer
the financial instrument to the cus 'v'OL 5 ‘JC 9 tomer and turn a profit as the mar—
ket evolves in unknown ways. Months if not years before, the
derivatives group may decide that
a demand exists for a new deriva
tive product due to client inquiries,
news of competitors offering such
a product, or the brainchild of the
sales team bminstorming with the
quantitative team. Whatever the ori—
gin, the question then arises
whether this product can be offered
and can be proﬁtable. To answer this
requires modeling. FRO/V1 l995 TO 2004 TH DAlLY TURNOVER l
lNTEREST RATE DERIVATIVE
GREW STEADJ'LY FROM $ 1' 5i
BlLLiON TO $l.025 TRlLLiON, REPRESENTFNG AN ANNUA RATE OF iNCREASE OF OVE
2 l %. The quantitative team must
devise mathematical models that
relate the underlying instrument
variables to the value of the deriv
ative contract. These models mttst
be thoroughly tested in a variety of
scenarios and under a variety of cir—
cumstances. The whole team must
be educated on how the models
work. The...
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