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Derivatives - TAX REGULATION FINANCE APRlL 2005 VOL 5 NO 8...

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Unformatted text preview: TAX ' REGULATION - FINANCE % APRlL 2005 VOL 5, NO 8 WG 6-13 ' 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 would-be, want-to—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 end-users— 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 short-term 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 per-7 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 rpfxO-ipdf. 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 two-way 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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