Quantitative analyst - AbsoluteAstronomy.com

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

Investment management

Investment management is the professional management of various securities and assets in order to meet specified investment goals for the benefit of the investors...

, risk management

Risk management

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

and derivatives

Derivative (finance)

A derivative instrument is a contract between two parties that specifies conditions—in particular, dates and the resulting values of the underlying variables—under which payments, or payoffs, are to be made between the parties.Under U.S...

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

Statistical arbitrage

In the world of finance and investments, statistical arbitrage is used in two related but distinct ways:* In academic literature, "statistical arbitrage" is opposed to arbitrage. In deterministic arbitrage, a sure profit can be obtained from being long some securities and short others...

, algorithmic trading

Algorithmic trading

In electronic financial markets, algorithmic trading or automated trading, also known as algo trading, black-box trading or robo trading, is the use of electronic platforms for entering trading orders with an algorithm deciding on aspects of the order such as the timing, price, or quantity of the...

, and electronic market making.

History

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

Harry Markowitz

Harry Markowitz

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

'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

Ito calculus

Itō calculus, named after Kiyoshi Itō, extends the methods of calculus to stochastic processes such as Brownian motion . It has important applications in mathematical finance and stochastic differential equations....

, management of risk in a quantifiable manner underlies much of the modern theory.

In 1969 Robert Merton

Robert C. Merton

Robert Carhart Merton is an American economist, Nobel laureate in Economics, and professor at the MIT Sloan School of Management.-Biography:...

introduced stochastic calculus

Stochastic calculus

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...

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

Fischer Black

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

and Myron Scholes

Myron Scholes

Myron Samuel Scholes is a Canadian-born American financial economist who is best known as one of the authors of the Black–Scholes equation. In 1997 he was awarded the Nobel Memorial Prize in Economic Sciences for a method to determine the value of derivatives...

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 as a result, showed how to price numerous other "derivative" securities.

Education

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 object oriented computer programming, most commonly C++

C++

C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...

and/or Java

Java (programming language)

Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...

.

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

Mathematical finance

Mathematical finance is a field of applied mathematics, concerned with financial markets. The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory. Generally, mathematical finance will derive and extend the mathematical...

, computational finance

Computational finance

Computational finance, also called financial engineering, is a cross-disciplinary field which relies on computational intelligence, mathematical finance, numerical methods and computer simulations to make trading, hedging and investment decisions, as well as facilitating the risk management of...

, and/or financial reinsurance

Financial reinsurance

Financial Reinsurance , is a form of reinsurance which is focused more on capital management than on risk transfer. In the non-life segment of the insurance industry this class of transactions is often referred to as finite reinsurance....

. In particular, Masters degrees in mathematical finance

Mathematical finance

, financial engineering, and financial analysis

Financial analysis

Financial analysis refers to an assessment of the viability, stability and profitability of a business, sub-business or project....

are becoming more popular with students and with employers. See Master of Quantitative Finance

Master of Quantitative Finance

A masters degree in quantitative finance concerns the application of mathematical methods to the solution of problems in financial economics. There are several like-titled degrees which may further focus on financial engineering, financial risk management, computational finance and/or mathematical...

; Master of Financial Economics

Master of Financial Economics

A master’s degree in financial economics provides an understanding of theoretical finance and the underlying economic framework. The degree is postgraduate, and may incorporate a thesis or research component. Programs are often a joint offering by the business school and the economics department;...

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

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 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

Signal processing

Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

, game theory

Game theory

Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...

, gambling Kelly criterion

Kelly criterion

In probability theory, the Kelly criterion, or Kelly strategy or Kelly formula, or Kelly bet, is a formula used to determine the optimal size of a series of bets. In most gambling scenarios, and some investing scenarios under some simplifying assumptions, the Kelly strategy will do better than any...

, market micro structure, econometrics

Econometrics

Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...

, and time series

Time series

In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...

analysis. Algorithmic trading

Algorithmic trading

includes statistical arbitrage

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

Latency

Latency or latent may refer to:*Latency period , the time between exposure to a pathogen, chemical or radiation, and when symptoms first become apparent...

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

Value at risk

In financial mathematics and financial risk management, Value at Risk is a widely used risk measure of the risk of loss on a specific portfolio of financial assets...

, and this is backed up with various forms of stress testing and direct analysis of the positions and models used by traders.

Innovation

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 equation

Partial differential equation

In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

s, 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 equation

Partial differential equation

s, and solutions to these based upon numerical analysis

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

.

The most commonly used numerical methods are:

Finite difference method
Finite difference method
In mathematics, finite-difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.- Derivation from Taylor's polynomial :...

– used to solve partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

s;
Monte Carlo method
Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...

– Also used to solve partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

s, but Monte Carlo simulation is also common in risk management.

Techniques

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

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
Backtesting
Backtesting is the process of evaluating a strategy, theory, or model by applying it to historical data. Backtesting can be used in situations like studying how a trading method would have performed in past stock markets or how a model of climate and weather patterns would have matched past...
Credit analysis

Seminal publications

1900 - Louis Bachelier
Louis Bachelier
-External links:** Louis Bachelier webpage at the Université de Franche-Comté, Besançon / France. Text in French.** also from Index Funds Advisors, this discussion of...

, Théorie de la spéculation
1952 - Harry Markowitz
Harry Markowitz
Harry Max Markowitz is an American economist and a recipient of the John von Neumann Theory Prize and the Nobel Memorial Prize in Economic Sciences....

, Portfolio Selection, Modern portfolio theory
Modern portfolio theory
Modern portfolio theory is a theory of investment which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets...
1956 - John Kelly
John Larry Kelly, Jr
John Larry Kelly, Jr. , was a scientist who worked at Bell Labs. He is best known for formulating the Kelly criterion, an algorithm for maximally investing money....

, A New Interpretation of Information Rate
1967 - Edward O. Thorp
Edward O. Thorp
Edward Oakley Thorp is an American mathematics professor, author, hedge fund manager, and blackjack player. He was a pioneer in modern applications of probability theory, including the harnessing of very small correlations for reliable financial gain.He was the author of Beat the Dealer, the first...

and Sheen Kassouf, Beat the Market
1972 - Eugene Fama
Eugene Fama
Eugene Francis "Gene" Fama is an American economist, known for his work on portfolio theory and asset pricing, both theoretical and empirical. He is currently Robert R...

and Merton Miller
Merton Miller
Merton Howard Miller was the co-author of the Modigliani-Miller theorem which proposed the irrelevance of debt-equity structure. He shared the Nobel Memorial Prize in Economic Sciences in 1990, along with Harry Markowitz and William Sharpe...

, Theory of Finance
1973 - Fischer Black
Fischer Black
Fischer Sheffey Black was an American economist, best known as one of the authors of the famous Black–Scholes equation.-Background:...

and Myron Scholes
Myron Scholes
Myron Samuel Scholes is a Canadian-born American financial economist who is best known as one of the authors of the Black–Scholes equation. In 1997 he was awarded the Nobel Memorial Prize in Economic Sciences for a method to determine the value of derivatives...

, The Pricing of Options and Corporate Liabilities and Robert C. Merton
Robert C. Merton
Robert Carhart Merton is an American economist, Nobel laureate in Economics, and professor at the MIT Sloan School of Management.-Biography:...

, Theory of Rational Option Pricing, Black–Scholes
1976 - Fischer Black
Fischer Black
Fischer Sheffey Black was an American economist, best known as one of the authors of the famous Black–Scholes equation.-Background:...

, The pricing of commodity contracts, Black model
Black model
The Black model is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing bond options, interest rate caps / floors, and swaptions...
1977 - Phelim Boyle
Phelim Boyle
Phelim Boyle , a distinguished professor and actuary, is a professor of finance in the Laurier School of Business & Economics at Wilfrid Laurier University in Canada and is a pioneer of quantitative finance. He is best known for initiating the use of Monte Carlo methods in option pricing...

, Options: A Monte Carlo Approach, Monte Carlo methods for option pricing
1977 - Oldrich Vasicek
Oldrich Vasicek
Oldrich Alfons Vasicek a Czech mathematician, received his master's degree in math from the Czech Technical University, 1964, and a doctorate in probability theory from Charles University four years later....

, An equilibrium characterisation of the term structure, Vasicek model
Vasicek model
In finance, the Vasicek model is a mathematical model describing the evolution of interest rates. It is a type of "one-factor model" as it describes interest rate movements as driven by only one source of market risk...
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
Jonathan E. Ingersoll
Jonathan Edwards "Jon" Ingersoll, Jr. is an American economist. He is currently the Adrian C. Israel Professor at Yale School of Management, having previously taught at the University of Chicago....

and Stephen Ross
Stephen Ross
Stephen Ross may refer to:* Stephen Jay Ross , U.S. communications businessman* Stephen Ross, Baron Ross of Newport , former Liberal Member of Parliament* Stephen Ross , financial economist and textbook author...

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

, Emanuel Derman
Emanuel Derman
Emanuel Derman is a South African-born academic, businessman and writer. He is best known as a quantitative analyst, and author of the book My Life as A Quant: Reflections on Physics and Finance....

and William Toy, A One-Factor Model of Interest Rates and Its Application to Treasury Bond, Black-Derman-Toy model
1992 - Fischer Black
Fischer Black
Fischer Sheffey Black was an American economist, best known as one of the authors of the famous Black–Scholes equation.-Background:...

and Robert Litterman: Global Portfolio Optimization, Financial Analysts Journal, September 1992, pp. 28–43 Black-Litterman model
Black-Litterman model
In Finance the Black–Litterman model is a mathematical model for portfolio allocation developed in 1990 at Goldman Sachs by Fischer Black and Robert Litterman, and published in 1992. It seeks to overcome problems that institutional investors have encountered in applying modern portfolio theory in...
1995 - Richard Grinold and Ronald Kahn, Active Portfolio Management: Quantitative Theory and Applications
1996 - Philippe Jorion, Value at risk
Value at risk
In financial mathematics and financial risk management, Value at Risk is a widely used risk measure of the risk of loss on a specific portfolio of financial assets...
1997 - Espen Gaarder Haug, The Complete Guide to Option Pricing Formulas
1998 - Paul Wilmott
Paul Wilmott
Paul Wilmott is a researcher, consultant and lecturer in quantitative finance. He is best known as the author of various academic and practitioner texts on risk and derivatives, and for Wilmott magazine and Wilmott.com , a quantitative finance portal....

, Derivatives: The Theory and Practice of Financial Engineering
2004 - Emanuel Derman
Emanuel Derman
Emanuel Derman is a South African-born academic, businessman and writer. He is best known as a quantitative analyst, and author of the book My Life as A Quant: Reflections on Physics and Finance....

, My Life as a Quant: Reflections on Physics and Finance
2004 - Steven E. Shreve
Steven E. Shreve
Steven E. Shreve is a mathematician and currently the Orion Hoch Professor of Mathematical Sciences at Carnegie Mellon University and the author of several major books on the mathematics of financial derivatives....

, Stochastic Calculus for Finance

External links

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.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

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

History

Education

Front office quantitative analyst

Quantitative investment management

Library quantitative analysis

Algorithmic trading quantitative analyst

Risk management

Innovation

Model validation

Quantitative developer

Mathematical and statistical approaches

Techniques

Areas of work

Seminal publications

See also

Further reading

External links