Program in Quantitative Finance

Applied Mathematics and Statistics

Stony Brook University

Career Guide

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This guide is a resource for students and advisors. If you are new to the subject area you may find many unfamiliar terms. We suggest that you turn to the material under External Resources and Recommended Texts for help. We have attempted to give a broad representation, and we make no claims of completeness.


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Perspectives on Financial Markets


We'll try to give a gentle, and somewhat idiosyncratic, introduction to finance and financial markets by looking at them from a number of different perspectives. As mentioned earlier, we make no pretense of completeness and readers are encouraged to follow up with readings from other sources.

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Financial Instruments


Financial instruments or securities are essentially contracts which package capital or wealth in a tradeable form. Financial markets are the "places" in which the buyers and sellers of financial instruments meet. Sometimes this occurs in an actual physical location such as the New York Stock Exchange, within a virtual space such as the NASDAQ or in a decentralized fashion such as certain over-the-counter or OTC markets.


What are sometimes called underlying securities (This choice of terminology will become clearer shortly.) fall into three broad categories:


  • Equities - Sometimes called shares, equities represent ownership,
  • Debt - Debt instruments represent claims against capital and
  • Currencies - The units of money for a nation are its currency.


An example of an equity security is common stock which represent shares of ownership of a corporation. Long-term debt is often represented by a bond in which a corporation sells a bond in return for agreeing to pay the purchaser a series of interest payments over a fixed term at the end of which the original amount loaned is returned. International trade involves dealing in more than one nation's currency and the foreign exchange markets are organized to accomplish this.


A derivative security is a security whose price is determined by the price of some underlying asset or security. We'll cover two of the simpler examples:


  • Forward Contract or Future - A forward contract or future is the obligation to buy or sell a certian quantity of an asset or security at a fixed time in the future.
  • Option - An option is the right but not the obligation to undertake a financial transaction at or by a specified date for a specified price.


Derivatives were originally developed as a means of controlling risk. For example, an airline concerned about the possibilty of a price increase in jet fuel could enter into a futures contract today to receive a fixed amount of fuel sometime in the future. The other side of the trade, to deliver that fuel, might be taken by an oil company concerned about the possibility of a price drop. The contract insulates them against price changes and allows them to plan and price their operations with less risk.


Derivatives generally require less capital than direct investment in the underlying. Thus, they can also be used by speculators to make pure bets on price movements. The structure of derivatives can become quite complex and much of quantitative finance is concerned with designing and pricing them.

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Market Participants


Another way to understand financial markets is by examining the roles of its participants. The most common role is taken up by investors who seek to participate in the economic activity of society by purchasing either units of ownership (e.g., stocks) or by loaning money (bonds). On the other side are issuers who offer such financial instruments in order to raise capital for their operations. Facilitating such exchanges are investment bankers who help to structure such instruments and bring the issuers and investors together.


This initial issuance is done on what is called the primary market. Of course, once such instruments have been issued they can be sold on what is called the secondary market or after market. For example, stockholderes who themselves need capital or who believe their stocks are overvalued can sell them to other investors in the secondary market.


Within the financial markets that are organized to bring investor and issuers together traders enter the picture. Some traders are speculators who are not focused on the long-term economic income or growth, but in exploiting short-term movements in prices, e.g., due to local supply and demand imbalances. Others are hedgers who trade financial instruments in order to reduce their risk, in effect buying insurance against some possible, undesirable, future outcome. Finally, there are arbitrageurs who buy and sell related instruments whose prices are inconsistent with one another.

Facilitating such trading activity are market makers, brokers and banks whose role it is to maintain inventories of financial instruments and bring buyers and sellers together in an orderly fashion.

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Careers in Quantitative Finance


There are many overlaps and synergies in the activities listed below; nevertheless, most quant positions have a specific focus within the firm: to make money by trading the firm’s own capital, to support the frontline traders, to create new financial products, to measure and control risk, or maintain investment portfolios that meet certain objectives. and so forth.


Associated with each area of practice are many complex problems that still remain to be solved. These represent opportunities for researchers in both academia and industry.

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Alternative Investments and Proprietary Trading


Proprietary trading in alternative investments is trading done for the direct benefit of the owners of the firm; this is opposed to agency trading which is trading done for the benefit of its customers. Traditional financial institutions often engage in proprietary trading as an important sideline. Hedge funds, typically organized as limited partnerships, do so as their primary business activity.


Among the alternative investment strategies are convertible arbitrage, various forms of leveraged long-short equity, emerging markets, distressed debt, merger arbitrage, fixed income arbitrage, global macro, managed futures, and private equity. Within each category, there are typically sub-categories. As examples, convertible arbitrage can be broken down into capital structure arbitrage, mandatory converts, synthetic puts, volatility arbitrage, and credit arbitrage; long-short equity can be broken down into general long-short equity, dedicated short bias and equity market neutral.

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Trading Support


For trading desks, pricing complex instruments and transactions rapidly and accurately while simultaneously managing risk in manner consistent with firm-wide objectives are critical capabilities. Quantitative analysts provide the mathematical talent required to build and maintain these decision support systems. Both proprietary implementations built in-house and commercial systems sold as turnkey solutions are used. The trading activities themselves may either be proprietary or customer related.


The precise manner in which "quants" are integrated into the trading desk varies from case to case. If a desk is executing trades output from an automated system, then the objective is often not what to trade but how to execute with minimal impact on the market. In contrast, a market maker must match incoming buys and sells and often commits its own capital to maintain an orderly market; in todays markets, volumes are so high and trades are executed so quickly that this cannot be accomplished without analytic support. In other cases, traders operate in areas without well organized exchanges, such a mortgage backed securities, and must be able to run complex models to price these instruments as they negotiate with counterparties.

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Consulting and Customer Support


On the sell side investment banks and other financial institutions provide research reports and other forms of analytical support to their customers. These supports may be provided gratis as a means of maintaining client relationships or stimulating the demand for a firm’s services. A visit to any number of brokerage websites will give you an indication of how pervasive this is.


In other cases, these services may be paid for by the investing organization itself. Companies, universities and other organziations maintain significant portfolios of financial assets in the form of pension funds, endownments and sinking funds (monies set aside to fund an activity or purchase in the future). Smaller firms hire outside consultants to advise them in the management these assets. Larger organizations maintain their own staff of professionals, though they still may use consultants to provide an independent review.

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Product Development


An increasing share of the business undertaken by investment banks has been in the form of exotic options, hybrid securities and collateralized obligations. These products are used to enhance return or to insure against legal, fiscal, regulatory or liquidity risks—some of which are company specific and may require customized solutions.


An example has been the development of collateralized obligations. The most common of these are mortgage-backed securities (MBSs), which break apart a payment stream into sub-deals or tranches, e.g., separating the principal and interest streams, POs and IOs, respectively. In turn, derivatives of these tranches can be created, e.g., in which the yield from a fixed rate IO is swapped with a floating rate.


Other examples include hybrid securities that overlay various fixed income or equity investments with derivatives to enhance yield or create a more tax efficient income stream. For example, a debtor can combine a fixed rate bond with a receiver swaption to give an issuer the benefits of both a fixed and floating rate bond. This structure allows the issuer to retain fixed rate payments if rates rise but switch to floating rate payments if rates fall, albeit with an “insurance” cost.


These products involve complex provisions and are difficult to price. They often demand the assessment of events and probabilities for which there is no or only an illiquid “market”. This difficulty, however, is an opportunity. Financial institutions are in a better position to model these instruments, trade them at an attractive spread, and, as counterparties to many such deals, build internal portfolios whose component risks offset one another.

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Risk Control


Laws and regulations dealing with credit and captial requirements have been around for decades, in certain forms for centuries. However, recent catastrophic, high profile failures of hedge funds and investment banks have led to a call for a more consistent, verifiable, quantitative, firm-wide approach to risk monitoring and control. Firms now recognize that, with the increasing complexity of financial products and markets, the organization's survival depends upon being able to define and enforce coherent risk management policies.


Defining, developing, implementing, operating and maintaining the necessary infrastructure to accomplish this is a demanding task. It requires a deep understanding of a wide spectrum of financial instruments and how exposure to them is financed. There are also significant technical challenges in real-time processing, high performance databases, and visualization.

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Portfolio Management


Portfolio management deals with the identification of financial objectives and their translation into a portfolio of assets that must be managed over time in the face of uncertain investment performance and consumption demands. This is no simple task: There are thousands of potential investments related to one another in complex ways, an enormous number of parameters which must be estimated in a statistically meaningful fashion, and a system of operational, business and legal goals and requirements which must be expressed in a consistent mathematical framework.


Once this foundation has been set down, the challenges associated with making the choice of assets in a portfolio are formidable. Even with the guidance of existing theory, there are many real world issues that complicate the solutions. We are dealing with underlying parameters that are nonstationary and poorly understood and with transactions costs that are highly nonlinear and uncertain. Such complications, in turn, mean that standard single period approaches may be only poor representations of the actual problem.


Individuals in this area may work either as in-house portfolio managers or as outside consultants. Large portfolios such pension funds, corporate sinking funds, and university endowments typically employ both in-house and consulting talent. However, all investors, even individuals managing their 401(k)s, require these services.

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Academic and Industrial Research


There are practical problems that must be solved “well enough” to allow the players in financial markets and in the financial service industries to operate but for which the best available approaches involve compromises that employ oversimplified models because of limitations of theory, available data or computational resources. Modern theories, despite their elegance and utility, fail to adequately account for many of the nuances of real markets. These limitations represent opportunities for the academic or industrial researcher.

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Texts to Help Your Career


Advice, from any quarter, needs to taken with a grain of salt. Nevertheless, it is useful to read the ideas and experiences of those who have gone before you.

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Career Advice, Biographies and Histories


  • Bookstaber, Richard, A Demon of  Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation, Wiley, 2007.


  • Derman, Emmanuel, My Life as a Quant: Reflections on Physics and Finance, Wiley, 2004.


  • Jui, Brett, Starting Your Career as a Wall Street Quant, Outskirts Press, 2007.


  • Schachter, Barry, and Richard R.Lindsey, eds., How I Became a Quant: Insights from 25 of Wall Street's Elite, Wiley, 2007.

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Résumé and Interview Help


  • Crack, Timothy Falcon, Heard on the Street: Quantitative Questions fromWall Street Job Interviews, Crack, 2007.


  • Wilmott, Paul, Frequently Asked Questions in Quantitative Finance, Wiley, 2007.


  • Voitle, Jennifer, Vault Guide to Advanced Finance & Quantitative Interviews, Vault, 2002.

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