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. See List of quantitative analysts.
Although the original quantitative analysts 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.
Quantitative finance started in the U.S. in the 1970s as some astute investors began using mathematical formulas 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 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.
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 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.
Quantitative analysts often come from physics, engineering, or mathematics backgrounds rather than economics-related fields, and quantitative analysis is a major source of employment for people with physics and mathematics Ph.Ds. Typically, a quantitative analyst will also need extensive skills in computer programming, most commonly C++ and/or Java.
This demand for quantitative analysts 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 reinsurance. In particular, Masters degrees in mathematical finance, financial engineering, Operations Research and financial analysis are becoming more popular with students and with employers. See Master of Quantitative Finance; Master of Financial Economics.
Types of quantitative analyst 
Front office quantitative analyst 
In trading and sales operations, 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 modelling. 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 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 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 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 methods and finite difference methods, as well as the nature of the products being modelled.
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 testing and direct analysis of the positions and models used by traders.
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 through continuous improvement and thought leadership. This has led to the creation of collaborative environments in order to produce the most robust statistical models available. Through working with a large pool of some of the world's most talented quantitative analysts, economists and mathematicians from the financial industry and academia, transparency continues to be improved, leading to constant improvement.
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 quantitative analysts 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 quantitative analyst will typically earn a fraction of quantitative analysts in other groups with similar length of experience.
Quantitative developer 
Quant developers are computer specialists that assist, implement and maintain the quant models. They tend to be highly specialised language technicians that bridge the gap between IT and quantitative analysts.
Mathematical and statistical approaches 
Because of their backgrounds, quantitative analysts draw from three forms of mathematics: statistics and probability, calculus centered around partial differential equations, and econometrics. The majority of quantitative analysts 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 quantitative analysts tend to have more of a reliance on numerical analysis, and less of a reliance on statistics and econometrics. These quantitative analysts 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 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.
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. Thorp and Sheen Kassouf, Beat the Market
- 1972 - Eugene Fama and Merton Miller, Theory of Finance
- 1973 - Fischer Black and Myron 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, Jonathan 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
- 2004 - Emanuel Derman, My Life as a Quant: Reflections on Physics and Finance
- 2004 - Steven E. Shreve, Stochastic Calculus for Finance
See also 
- Bachelier Finance Society
- Society of Quantitative Analysts
- List of quantitative analysts
- Mathematical finance
- Financial modeling
- Master of Quantitative Finance
Further reading 
- Bernstein, Peter L. (1992) Capital Ideas: The Improbable Origins of Modern Wall Street
- Bernstein, Peter L. (2007) Capital Ideas Evolving
- Derman, Emanuel (2007) My Life as a Quant ISBN 0-470-19273-9 [Amazon-US | Amazon-UK]
- Patterson, Scott D. (2010). The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It. Crown Business, 352 pages. ISBN 0-307-45337-5 [Amazon-US | Amazon-UK] ISBN 978-0-307-45337-2 [Amazon-US | Amazon-UK]. Amazon page for book via Patterson and Thorp interview on Fresh Air, Feb. 1, 2010, including excerpt "Chapter 2: The Godfather: Ed Thorp". Also, an excerpt from "Chapter 10: The August Factor", in the January 23, 2010 Wall Street Journal.
- Reid, Colin (2012) Rise of the Quants: (Great Minds in Finance Series) ISBN 023027417X [Amazon-US | Amazon-UK]
- http://sqa-us.org - Society of Quantitative Analysts
- http://www.q-group.org/—Q-Group Institute for Quantitative Research in Finance
- http://cqa.org - CQA—Chicago Quantitative Alliance
- http://prmia.org - PRMIA—Professional Risk Managers Industry Association
- http://iafe.org - International Association of Financial Engineers
- http://www.lqg.org.uk/ - London Quant Group
- http://www.quantnet.com - Education Resource for Financial Engineering, featuring career guide, interviews with famous quants, online forum
- http://www.wilmott.com - famed mainly for its forums, one of the main places where quants talk online.
- http://quant.stackexchange.com - question and answer site for quantitative finance