Quantitative analyst

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A quantitative analyst (or, in financial jargon, a quant) is a person who specializes in the application of mathematical and statistical methods to financial and risk management problems. The occupation is similar to those in industrial mathematics in other industries. [1]


Although the original quantitative analysts were "sell side quants" from market maker firms, concerned with derivatives pricing and risk management, the meaning of the term has expanded over time to include those individuals involved in almost any application of mathematics in finance, including the buy side. [2] Examples include statistical arbitrage, quantitative investment management, algorithmic trading, and electronic market making.

Sell side is a term used in the financial services industry. The three main markets for this selling are the stock, bond, and foreign exchange market. It is a general term that indicates a firm that sells investment services to asset management firms, typically referred to as the buy side, or corporate entities. One important note, the sell side and the buy side work hand in hand and each side could not exist without the other. These services encompass a broad range of activities, including broking/dealing, investment banking, advisory functions, and investment research.

Derivative (finance) financial instrument whose value is based on one or more underlying assets

In finance, a derivative is a contract that derives its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying." Derivatives can be used for a number of purposes, including insuring against price movements (hedging), increasing exposure to price movements for speculation or getting access to otherwise hard-to-trade assets or markets. Some of the more common derivatives include forwards, futures, options, swaps, and variations of these such as synthetic collateralized debt obligations and credit default swaps. Most derivatives are traded over-the-counter (off-exchange) or on an exchange such as the New York Stock Exchange, while most insurance contracts have developed into a separate industry. In the United States, after the financial crisis of 2007–2009, there has been increased pressure to move derivatives to trade on exchanges. Derivatives are one of the three main categories of financial instruments, the other two being stocks and debt. The oldest example of a derivative in history, attested to by Aristotle, is thought to be a contract transaction of olives, entered into by ancient Greek philosopher Thales, who made a profit in the exchange. Bucket shops, outlawed a century ago, are a more recent historical example.

Risk management Set of measures for the systematic identification, analysis, assessment, monitoring and control of risks

Risk management is the identification, evaluation, and prioritization of risks followed by coordinated and economical application of resources to minimize, monitor, and control the probability or impact of unfortunate events or to maximize the realization of opportunities.


Robert C. Merton, one of the pioneers of quantitative analysis, promoted stochastic calculus into the study of finance. Robert C. Merton.jpg
Robert C. Merton, one of the pioneers of quantitative analysis, promoted stochastic calculus into the study of finance.

Quantitative finance started in 1900 with Louis Bachelier's doctoral thesis Theory of Speculation, which provided a model to price options under a Normal Distribution.

Louis Bachelier Pioneer in mathematical economics

Louis Jean-Baptiste Alphonse Bachelier was a French mathematician at the turn of the 20th century. He is credited with being the first person to model the stochastic process now called Brownian motion, as part of his PhD thesis The Theory of Speculation.

Option (finance) right to to buy or sell a certain thing at a later date at an agreed price

In finance, an option is a contract which gives the buyer the right, but not the obligation, to buy or sell an underlying asset or instrument at a specified strike price prior to or on a specified date, depending on the form of the option. The strike price may be set by reference to the spot price of the underlying security or commodity on the day an option is taken out, or it may be fixed at a discount or at a premium. The seller has the corresponding obligation to fulfill the transaction – to sell or buy – if the buyer (owner) "exercises" the option. An option that conveys to the owner the right to buy at a specific price is referred to as a call; an option that conveys the right of the owner to sell at a specific price is referred to as a put. Both are commonly traded, but the call option is more frequently discussed.

Harry Markowitz's 1952 doctoral thesis "Portfolio Selection" and its published version was one of the first efforts in economics journals to formally adapt mathematical concepts to finance (mathematics was until then confined to mathematics, statistics or specialized economics journals). [3] Markowitz formalized a notion of mean return and covariances for common stocks which allowed him to quantify the concept of "diversification" in a market. He showed how to compute the mean return and variance for a given portfolio and argued that investors should hold only those portfolios whose variance is minimal among all portfolios with a given mean return. Although the language of finance now involves Itō calculus, management of risk in a quantifiable manner underlies much of the modern theory.

Harry Max Markowitz is an American economist, and a recipient of the 1989 John von Neumann Theory Prize and the 1990 Nobel Memorial Prize in Economic Sciences.

Thesis document submitted in support of candidature for an academic degree

A thesis or dissertation is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings. In some contexts, the word "thesis" or a cognate is used for part of a bachelor's or master's course, while "dissertation" is normally applied to a doctorate, while in other contexts, the reverse is true. The term graduate thesis is sometimes used to refer to both master's theses and doctoral dissertations.

In 1965 Paul Samuelson introduced stochastic calculus into the study of finance. [4] [5] In 1969 Robert Merton promoted continuous stochastic calculus and continuous-time processes. Merton was motivated by the desire to understand how prices are set in financial markets, which is the classical economics question of "equilibrium," and in later papers he used the machinery of stochastic calculus to begin investigation of this issue.

Paul Samuelson American economist

Paul Anthony Samuelson was an American economist and the first American to win the Nobel Memorial Prize in Economic Sciences. The Swedish Royal Academies stated, when awarding the prize in 1970, that he "has done more than any other contemporary economist to raise the level of scientific analysis in economic theory". Economic historian Randall E. Parker has called him the "Father of Modern Economics", and The New York Times considered him to be the "foremost academic economist of the 20th century".

Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly.

Robert C. Merton American economist

Robert Cox Merton is an American economist, Nobel Memorial Prize in Economic Sciences laureate, and professor at the MIT Sloan School of Management, known for his pioneering contributions to continuous-time finance, especially the first continuous-time option pricing model, the Black–Scholes formula. In 1993 Merton co-founded hedge fund Long-Term Capital Management. In 1997 he received the Nobel Prize for his contributions in Economics.

At the same time as Merton's work and with Merton's assistance, Fischer Black and Myron Scholes developed the Black–Scholes model, which was awarded the 1997 Nobel Memorial Prize in Economic Sciences. It provided a solution for a practical problem, that of finding a fair price for a European call option, i.e., the right to buy one share of a given stock at a specified price and time. Such options are frequently purchased by investors as a risk-hedging device. In 1981, Harrison and Pliska used the general theory of continuous-time stochastic processes to put the Black–Scholes model on a solid theoretical basis, and showed how to price numerous other derivative securities. [6]

Fischer Black American economist

Fischer Sheffey Black was an American economist, best known as one of the authors of the famous Black–Scholes equation.

Myron Scholes Canadian economist

Myron Samuel Scholes is a Canadian-American financial economist. Scholes is the Frank E. Buck Professor of Finance, Emeritus, at the Stanford Graduate School of Business, Nobel Laureate in Economic Sciences, and co-originator of the Black–Scholes options pricing model. Scholes is currently the chairman of the Board of Economic Advisers of Stamos Capital Partners. Previously he served as the chairman of Platinum Grove Asset Management and on the Dimensional Fund Advisors board of directors, American Century Mutual Fund board of directors and the Cutwater Advisory Board. He was a principal and limited partner at Long-Term Capital Management, L.P. and a managing director at Salomon Brothers. Other positions Scholes held include the Edward Eagle Brown Professor of Finance at the University of Chicago, senior research fellow at the Hoover Institution, director of the Center for Research in Security Prices, and professor of finance at MIT’s Sloan School of Management. Scholes earned his PhD at the University of Chicago.

The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price regardless of the risk of the security and its expected return. The formula led to a boom in options trading and provided mathematical legitimacy to the activities of the Chicago Board Options Exchange and other options markets around the world. It is widely used, although often with adjustments and corrections, by options market participants.

Emanuel Derman's 2004 book My Life as a Quant helped to both make the role of a quantitative analyst better known outside of finance, and to popularize the abbreviation "quant" for a quantitative analyst. [7]


Quantitative analysts often come from applied mathematics, physics or engineering backgrounds rather than economics-related fields, and quantitative analysis is a major source of employment for people with mathematics and physics PhD degrees, or with financial mathematics masters degrees. Typically, a quantitative analyst will also need extensive skills in computer programming, most commonly C, C++, Java, R, MATLAB, Mathematica, Python.

This demand for quantitative analysts has led to a resurgence in demand for actuarial qualifications as well as creation of specialized Masters and PhD courses in financial engineering, mathematical finance, computational finance, and/or financial reinsurance. In particular, Master's degrees in mathematical finance, financial engineering, operations research, computational statistics, machine learning, and financial analysis are becoming more popular with students and with employers. See Master of Quantitative Finance; Master of Financial Economics.

Data science and machine learning analysis and modelling methods are being increasingly employed in portfolio performance and portfolio risk modelling, [8] [9] and as such data science and machine learning Master's graduates are also in demand as quantitative analysts.


Front office quantitative analyst

In sales & trading, quantitative analysts work to determine prices, manage risk, and identify profitable opportunities. Historically this was a distinct activity from trading but the boundary between a desk quantitative analyst and a quantitative trader is increasingly blurred, and it is now difficult to enter trading as a profession without at least some quantitative analysis education. In the field of algorithmic trading it has reached the point where there is little meaningful difference. Front office work favours a higher speed to quality ratio, with a greater emphasis on solutions to specific problems than detailed modeling. FOQs typically are significantly better paid than those in back office, risk, and model validation. Although highly skilled analysts, FOQs frequently lack software engineering experience or formal training, and bound by time constraints and business pressures, tactical solutions are often adopted.

Quantitative investment management

Quantitative analysis is used extensively by asset managers. Some, such as FQ, AQR or Barclays, rely almost exclusively on quantitative strategies while others, such as Pimco, Blackrock or Citadel use a mix of quantitative and fundamental methods.

Library quantitative analysis

Major firms invest large sums in an attempt to produce standard methods of evaluating prices and risk. These differ from front office tools in that Excel is very rare, with most development being in C++, though Java and C# are sometimes used in non-performance critical tasks. LQs spend more time modeling ensuring the analytics are both efficient and correct, though there is tension between LQs and FOQs on the validity of their results. LQs are required to understand techniques such as Monte Carlo methods and finite difference methods, as well as the nature of the products being modeled.

Algorithmic trading quantitative analyst

Often the highest paid form of Quant, ATQs make use of methods taken from signal processing, game theory, gambling Kelly criterion, market microstructure, econometrics, and time series analysis. Algorithmic trading includes statistical arbitrage, but includes techniques largely based upon speed of response, to the extent that some ATQs modify hardware and Linux kernels to achieve ultra low latency.

Risk management

This has grown in importance in recent years, as the credit crisis exposed holes in the mechanisms used to ensure that positions were correctly hedged, though in no bank does the pay in risk approach that in front office. A core technique is value at risk, and this is backed up with various forms of stress test (financial), economic capital analysis and direct analysis of the positions and models used by various bank's divisions.


In the aftermath of the financial crisis, there surfaced the recognition that quantitative valuation methods were generally too narrow in their approach. An agreed upon fix adopted by numerous financial institutions has been to improve collaboration.

Model validation

Model validation (MV) takes the models and methods developed by front office, library, and modeling quantitative analysts and determines their validity and correctness. The MV group might well be seen as a superset of the quantitative operations in a financial institution, since it must deal with new and advanced models and trading techniques from across the firm. Before the crisis however, the pay structure in all firms was such that MV groups struggle to attract and retain adequate staff, often with talented quantitative analysts leaving at the first opportunity. This gravely impacted corporate ability to manage model risk, or to ensure that the positions being held were correctly valued. An MV quantitative analyst would typically earn a fraction of quantitative analysts in other groups with similar length of experience. In the years following the crisis, this has changed. Regulators now typically talk directly to the quants in the middle office such as the model validators, and since profits highly depend on the regulatory infrastructure, model validation has gained in weight and importance with respect to the quants in the front office.

Quantitative developer

Quantitative developers are computer specialists that assist, implement and maintain the quantitative models. They tend to be highly specialised language technicians that bridge the gap between software developer and quantitative analysts.

Mathematical and statistical approaches

Because of their backgrounds, quantitative analysts draw from various forms of mathematics: statistics and probability, calculus centered around partial differential equations, linear algebra, discrete mathematics, and econometrics. Some on the buy side may use machine learning. The majority of quantitative analysts have received little formal education in mainstream economics, and often apply a mindset drawn from the physical sciences. Quants use mathematical skills learned from diverse fields such as computer science, physics and engineering. These skills include (but are not limited to) advanced statistics, linear algebra and partial differential equations as well as solutions to these based upon numerical analysis.

Commonly used numerical methods are:


A typical problem for a mathematically oriented quantitative analyst would be to develop a model for pricing, hedging, and risk-managing a complex derivative product. These quantitative analysts tend to rely more on numerical analysis than statistics and econometrics. The mindset is to prefer a deterministically "correct" answer, as once there is agreement on input values and market variable dynamics, there is only one correct price for any given security (which can be demonstrated, albeit often inefficiently, through a large volume of Monte Carlo simulations).

A typical problem for a statistically oriented quantitative analyst would be to develop a model for deciding which stocks are relatively expensive and which stocks are relatively cheap. The model might include a company's book value to price ratio, its trailing earnings to price ratio, and other accounting factors. An investment manager might implement this analysis by buying the underpriced stocks, selling the overpriced stocks, or both. Statistically oriented quantitative analysts tend to have more of a reliance on statistics and econometrics, and less of a reliance on sophisticated numerical techniques and object-oriented programming. These quantitative analysts tend to be of the psychology that enjoys trying to find the best approach to modeling data, and can accept that there is no "right answer" until time has passed and we can retrospectively see how the model performed. Both types of quantitative analysts demand a strong knowledge of sophisticated mathematics and computer programming proficiency.

One of the principal mathematical tools of quantitative finance is stochastic calculus.

Academic and technical field journals

Areas of work

Seminal publications

See also

Related Research Articles

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  1. See Definition in the Society for Applied and Industrial Mathematics http://www.siam.org/about/pdf/brochure.pdf
  2. Derman, E. (2004). My life as a quant: reflections on physics and finance. John Wiley & Sons.
  3. Markowitz, H. (1952). "Portfolio Selection". Journal of Finance . 7 (1): 77–91. doi:10.1111/j.1540-6261.1952.tb01525.x.
  4. Samuelson, P. A. (1965). "Rational Theory of Warrant Pricing". Industrial Management Review. 6 (2): 13–32.
  5. Henry McKean the co-founder of stochastic calculus (along with Kiyosi Itô) wrote the appendix: see McKean, H. P. Jr. (1965). "Appendix (to Samuelson): a free boundary problem for the heat equation arising from a problem of mathematical economics". Industrial Management Review. 6 (2): 32–39.
  6. Harrison, J. Michael; Pliska, Stanley R. (1981). "Martingales and Stochastic Integrals in the Theory of Continuous Trading". Stochastic Processes and Their Applications. 11 (3): 215–260. doi:10.1016/0304-4149(81)90026-0.
  7. Derman, Emanuel (2004). My Life as a Quant. John Wiley and Sons.
  8. "Machine Learning in Finance: Theory and Applications". marketsmedia.com. 22 January 2013. Retrieved 2 April 2018.
  9. "A Machine-Learning View of Quantitative Finance" (PDF). qminitiative.org.
  10. "The Journal of Portfolio Management". jpm.iijournals.com. Retrieved 2019-02-02.
  11. http://www.tandfonline.com/toc/rquf20/current%7C
  12. "Finance and Stochastics – incl. Option to publish open access".

Further reading