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Quantitative analyst

A quantitative analyst is a person who works in finance using numerical or quantitative techniques. Similar work is done in most other modern industries, but the work is not always called quantitative analysis. In the investment industry, people who perform quantitative analysis are frequently called quants.

Although the original quants were concerned with investment management, risk management and derivatives pricing, the meaning of the term has expanded over time to include those individuals involved in almost any application of mathematics in finance. Examples include statistical arbitrage, algorithmic trading and electronic market making.



Robert C Merton, a pioneer of quantitative analysis, introduced stochastic calculus into the study of finance.

Quantative finance started in the U.S. in the 1970s as some astute investors began using mathematical formulae to price stocks and bonds.

Harry Markowitz’s 1952 Ph.D thesis "Portfolio Selection" was one of the first papers to formally adapt mathematical concepts to finance. Markowitz formalized a notion of mean return and co-variances 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 ITO calculus management of risk in a quantifiable manner underlies much of the modern theory.

In 1969 Robert Merton introduced stochastic calculus into the study of finance. 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.

At the same time as Merton's work and with Merton's assistance, Fischer Blackand Myron Scholes were developing their option pricing formula, which led to winning the 1997Nobel Prize in Economics. 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-Scholesoption pricing formula on a solid theoretical basis, and as a result, showed how to price numerous other "derivative" securities.


Quants often come from physics, engineering, or mathematics backgrounds rather than economics-related fields, and quant finance is a major source of employment for people with physics and mathematics Ph.D’s. Typically, a quant will also need extensive skills in computer programming, most commonly C++

This demand for quants has led to the 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 re-insuranceIn particular, Masters degrees in mathematical fiance, financial engineering and financial analysis are becoming more popular with students and with employers.

Types of Quant

Front Office Quant

In trading and sales operations, quants work to determine prices, manage risk, and identify profitable opportunities. Historically this was a distinct activity from trading but the boundary between a desk quant and a quant trader is increasingly blurred, and it is now difficult to enter trading as a profession without at least some quant 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 / quality ratio, with a greater emphasis on solutions to specific problems than detailed modelling. FOQs typically are significantly better paid than those in back office and risk, and in model validation. This has obvious implications for the quality of decisions at a strategic level. Although highly skilled programmers, FOQs are often bound by time constraints, and hacking complex tasks together using Excel and ad-hoc tools is not uncommon.

Quantitative Investment Management

Quantitative analysis used extensively by asset managers. Some, such as 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. Virtually all large asset managers and hedge funds rely to some degree on quantitative methods.

Library quant

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 modelling 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 methodsand finite differnce methods, as well as the nature of the products being modelled.

Algorithmic Trading Quant

Often the highest paid form of Quant, ATQs make use of methods taken fromsignal processing, game theory, gambling Kelly criterion, market micro structure, econometrics, and time series analysis. Algotrading 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 testing and direct analysis of the positions and models used by traders.

Model validation

MV takes the models and methods developed by front office, library, and modelling quants and determines their validity and correctness. The MV group might well be seen as a superset of the quant operations in a financial institution, since it must deal with new and advanced new models and trading techniques from across the firm. However, the pay structure in all firms is such that MV groups struggle to attract and retain adequate staff, often with talented quants leaving at the first opportunity. This gravely impacts corporate ability to manage model risk, or to ensure that the positions being held are correctly valued. An MV quant will typically earn a fraction of quants in other groups with similar length of experience.

Quantitative Developer

Although most quants spend the majority of their time programming and operating computers, there has emerged a specialism of implementing models so that the values may be calculated from market data. Whereas prototypes and early development may be in a mix of tools such as Matlaband R, most software is written in C++ for performance and better integration with existing systems.

Mathematical and statistical approaches

Because of their backgrounds, quants draw from three forms of mathematics: statistics and probability, calculus centered around partial differential equations and econometrics. The majority of quants have received little formal education in mainstream economics, and often apply a mindset drawn from the physical sciences. Physicists tend to have significantly less experience of statistical techniques, and thus lean on approaches based upon partial differential equations and solutions to these based upon numerical analysis. The most commonly used numerical methods are

  • Finite Difference Method Used to solve partial differential equations
  • Monte Carlo Method Also used to solve, partial differential equations but Monte Carlo simulation is also common in risk management


A typical problem for a numerically oriented quantitative analyst would be to develop a model for pricing, hedging, and risk-managing a complex derivative product. Mathematically-oriented quants tend to have more of a reliance on numerical analysis, and less of a reliance on statistics and econometrics. These quants tend to be of the psychology that prefers 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 quants 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 quants 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 quants demand a strong knowledge of sophisticated mathematics and computer programming proficiency.

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

Areas of work

  • Trading strategy development
  • Portfolio optimization
  • Derivatives pricing and hedging: involves a lot of highly efficient (usually object-oriented) software development, advanced numerical techniques, and stochastic calculus
  • Risk management: involves a lot of time series analysis, calibration, and backtesting Credit analysis



Seminal publications

  • 1900 –Louis Bachelier, Théorie de la spéculation
  • 1952 –Harry Markowitz, Portfolio Selection, Modern Portfolio Theory
  • 1956 –John Kelly, A New Interpretation of Information Rate
  • 1967 – Edward O. Thorpand Sheen Kassouf, Beat the Market
  • 1972 – Eugene Fama and Merton Miller, Theory of Finance
  • 1973 – Fischer Black andMyron Scholes, The Pricing of Options and Corporate Liabilities and Robert C. Merton, Theory of Rational Option Pricing, Black-Scholes 1976 –Fischer Black, The pricing of commodity contracts, Black Model
  • 1977 –Phelim Boyle, Options: A Monte Carlo Approach, Monte Carlo methods for option pricing. 1977 –Oldrich Vasicek, An equilibrium characterisation of the term structure, Vasicek model
  • 1980 - Lawrence G. McMillan, Options as a Strategic Investment
  • 1982 - Barr Rosenberg and Andrew Rudd, Factor-Related and Specific Returns of Common Stocks: Serial Correlation and Market Inefficiency’' Journal of Finance, May 1982 V. 37: #2
  • 1982 – Robert Engle Autoregressive Conditional Heteroskedasticity With Estimates of the Variance of U.K. Inflation, Seminal paper in ARCH family of models GARCH 1985 –John C. Cox, Jonathon E. Ingersoll and Stephen Ross, A theory of the term structure of interest rates, Cox-Ingersoll-Ross model
  • 1988 –John Hull, Options, futures, and other derivatives (7th edition issued in 2008)
  • 1990 –Fischer Black, Emanuel Derman and William Toy, A One-Factor Model of Interest Rates and Its Application to Treasury Bond, Black-Derman-Toy model
  • 1992 – Fischer Black and Robert Litterman: Global Portfolio Optimization, Financial Analysts Journal, September 1992, pp. 28–43 JSTOR 4479577 Black-Litterman model
  • 1995 - Richard Grinold and Ronald Kahn, Active Portfolio Management: Quantitative Theory and Applications
  • 1996 - Philippe Jorion, Value at Risk
  • 1997 – Espen Gaarder Haug The Complete Guide to Option Pricing Formulas
  • 1998 –Paul Wilmott, Derivatives: The Theory and Practice of Financial Engineering
  • 2004 –Emanuel Derman, My Life as a Quant: Reflections on Physics and Finance
  • 2004 –Steven E. Shreve, Stochastic Calculus for Finance


External links

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