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Quantitative analysis is the use of mathematical and statistical methods in
finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of f ...
and investment management. Those working in the field are quantitative analysts (quants). Quants tend to specialize in specific areas which may include
derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
structuring or pricing, risk management, investment management and other related finance occupations. The occupation is similar to those in
industrial mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemati ...
in other industries. The process usually consists of searching vast databases for patterns, such as correlations among liquid assets or price-movement patterns ( trend following or mean reversion). 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 mathematical finance, including the
buy side Buy-side is a term used in investment firms to refer to advising institutions concerned with buying investment services. Private equity funds, mutual funds, life insurance companies, unit trusts, hedge funds, and pension funds are the most common ...
. Applied quantitative analysis is commonly associated with quantitative investment management which includes a variety of methods such as statistical arbitrage, algorithmic trading and electronic trading. Some of the larger investment managers using quantitative analysis include Renaissance Technologies, D. E. Shaw & Co., and
AQR Capital Management AQR Capital Management (Applied Quantitative Research) is a global investment management firm based in Greenwich, Connecticut, United States. The firm, which was founded in 1998 by Cliff Asness, David Kabiller, John Liew, and Robert Krail, offers ...
.


History

Quantitative finance started in 1900 with Louis Bachelier's doctoral
thesis A thesis ( : theses), or dissertation (abbreviated diss.), is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings.International Standard ISO 7144 ...
"Theory of Speculation", which provided a model to price
options Option or Options may refer to: Computing *Option key, a key on Apple computer keyboards *Option type, a polymorphic data type in programming languages *Command-line option, an optional parameter to a command *OPTIONS, an HTTP request method ...
under a
normal distribution In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu ...
. 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 specialized economics journals). 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 Itô calculus, management of risk in a quantifiable manner underlies much of the modern theory. Modern quantitative investment management was first introduced from the research of Edward Thorp, a mathematics professor at New Mexico State University (1961–1965) and University of California, Irvine (1965–1977). Considered the "Father of Quantitative Investing", Thorp sought to predict and simulate blackjack, a card-game he played in Las Vegas casinos. He was able to create a system, known broadly as card counting, which used
probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...
and statistical analysis to successfully win blackjack games. His research was subsequently used during the 1980s and 1990s by investment management firms seeking to generate systematic and consistent returns in the U.S. stock market. The field has grown to incorporate numerous approaches and techniques; see ,
Post-modern portfolio theory Post-Modern Portfolio Theory (PMPT) is an extension of the traditional Modern Portfolio Theory (MPT), an application of mean-variance analysis (MVA). Both theories propose how rational investors can use diversification to optimize their portfolios. ...
, . In 1965 Paul Samuelson introduced stochastic calculus into the study of finance. 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. 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 The Nobel Memorial Prize in Economic Sciences, officially the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel ( sv, Sveriges riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne), is an economics award administered ...
. 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. The various
short-rate model A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written r_t \,. The short rate Under a s ...
s (beginning with Vasicek in 1977), and the more general HJM Framework (1987), relatedly allowed for an extension to fixed income and interest rate derivatives. Similarly, and in parallel, models were developed for various other underpinnings and applications, including
credit derivatives In finance, a credit derivative refers to any one of "various instruments and techniques designed to separate and then transfer the ''credit risk''" The Economist ''Passing on the risks'' 2 November 1996 or the risk of an event of default of a co ...
, exotic derivatives, real options, and employee stock options. Quants are thus involved in pricing and hedging a wide range of securities – asset-backed,
government A government is the system or group of people governing an organized community, generally a state. In the case of its broad associative definition, government normally consists of legislature, executive, and judiciary. Government i ...
, and corporate – additional to classic derivatives; see
contingent claim analysis In finance, a contingent claim is a derivative whose future payoff depends on the value of another “underlying” asset,Dale F. Gray, Robert C. Merton and Zvi Bodie. (2007). Contingent Claims Approach to Measuring and Managing Sovereign Credit R ...
. 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. After the
financial crisis of 2007–2008 Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of ...
, considerations re counterparty credit risk were incorporated into the modelling, previously performed in an entirely " risk neutral world", entailing three major developments; see : (i) Option pricing and hedging inhere the relevant volatility surface (to some extent, equity-option prices have incorporated the volatility smile since the 1987 crash) and banks then apply "surface aware" local- or stochastic volatility models; (ii) The risk neutral value is adjusted for the impact of counter-party credit risk via a
credit valuation adjustment Credit valuation adjustments (CVAs) are accounting adjustments made to reserve a portion of profits on uncollateralized financial derivatives. They are charged by a bank to a risky (capable of default) counterparty to compensate the bank for taking ...
, or CVA, as well as various of the other XVA; (iii) For discounting, the OIS curve is used for the "risk free rate", as opposed to
LIBOR The London Inter-Bank Offered Rate is an interest-rate average calculated from estimates submitted by the leading banks in London. Each bank estimates what it would be charged were it to borrow from other banks. The resulting average rate is u ...
as previously, and, relatedly, quants must model under a "
multi-curve framework In finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a "linear" IRD and one of the most liquid, benchmark products. It has associations wi ...
" ( LIBOR is due to be phased out by the end of 2021, with replacements including SOFR and TONAR, necessitating technical changes to the latter framework, while the underlying logic is unaffected).


Education

Quantitative analysts often come from financial mathematics, financial engineering,
applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemati ...
,
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
or
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...
backgrounds, and quantitative analysis is a major source of employment for people with financial mathematics master's degrees, or with mathematics and physics PhD degrees. Typically, a quantitative analyst will also need extensive skills in computer programming, most commonly C, C++,
Java Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's mo ...
, R,
MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementat ...
, Mathematica, and Python. Data science and
machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...
analysis and modelling methods are being increasingly employed in portfolio performance and portfolio risk modelling, and as such data science and machine learning Master's graduates are also hired as quantitative analysts. This demand for quantitative analysts has led to the creation of specialized Masters and PhD courses in financial engineering, mathematical finance,
computational finance Computational finance is a branch of applied computer science that deals with problems of practical interest in finance.Rüdiger U. Seydel, '' tp://nozdr.ru/biblio/kolxo3/F/FN/Seydel%20R.U.%20Tools%20for%20Computational%20Finance%20(4ed.,%20Sprin ...
, and/or
financial reinsurance Financial Reinsurance (or fin re), 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, Master's degrees in mathematical finance, financial engineering,
operations research Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decis ...
, computational statistics,
applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemati ...
,
machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...
, and financial analysis are becoming more popular with students and with employers. See
Master of Quantitative Finance A master's 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, computational fin ...
for general discussion. This has in parallel led to a resurgence in demand for actuarial qualifications, as well as commercial certifications such as the CQF. The more general Master of Finance (and Master of Financial Economics) increasingly includes a significant technical component.


Types


Front office quantitative analyst

In sales and 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. 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. See also structurer.


Quantitative investment management

:''See , for related articles.'' Quantitative analysis is used extensively by
asset managers Asset management is a systematic approach to the governance and realization of value from the things that a group or entity is responsible for, over their whole life cycles. It may apply both to tangible assets (physical objects such as buildings ...
. 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. One of the first quantitative investment funds to launch was based in Santa Fe, New Mexico and began trading in 1991 under the name Prediction Company. By the late-1990s, Prediction Company began using statistical arbitrage to secure investment returns, along with three other funds at the time, Renaissance Technologies and D. E. Shaw & Co, both based in New York. Prediction hired scientists and computer programmers from the neighboring
Los Alamos National Laboratory Los Alamos National Laboratory (often shortened as Los Alamos and LANL) is one of the sixteen research and development laboratories of the United States Department of Energy (DOE), located a short distance northwest of Santa Fe, New Mexico, ...
to create sophisticated statistical models using "industrial-strength computers" in order to " uildthe
Supercollider A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particl ...
of Finance".


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 Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's mo ...
, C# and Python 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 In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are ...
, 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 Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing '' signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...
,
game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
, gambling
Kelly criterion In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet), is a formula that determines the optimal theoretical size for a bet. It is valid when the expected returns are known. The Kelly bet size is found by maximizing the expe ...
, market microstructure,
econometrics Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. ...
, and
time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Ex ...
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 area has grown in importance in recent years, as the credit crisis exposed holes in the mechanisms used to ensure that positions were correctly hedged; see FRTB, . A core technique continues to be value at risk - applying both the parametric and "Historical" approaches, as well as Conditional value at risk and Extreme value theory - while this is supplemented with various forms of stress test, expected shortfall methodologies,
economic capital In finance, mainly for financial services firms, economic capital (ecap) is the amount of risk capital, assessed on a realistic basis, which a firm requires to cover the risks that it is running or collecting as a going concern, such as market ...
analysis, direct analysis of the positions at the desk level, and, as below, assessment of the models used by the bank's various divisions.


Innovation

In the aftermath of the financial crisis hich one?/sup>, 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; see
model risk In finance, model risk is the risk of loss resulting from using insufficiently accurate models to make decisions, originally and frequently in the context of valuing financial securities. However, model risk is more and more prevalent in activities ...
. 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. Post crisis, 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. 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 In finance, model risk is the risk of loss resulting from using insufficiently accurate models to make decisions, originally and frequently in the context of valuing financial securities. However, model risk is more and more prevalent in activities ...
, 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, as mentioned, this has changed.


Quantitative developer

Quantitative developers, sometimes called quantitative software engineers, or quantitative engineers, 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 engineers Software engineering is a systematic engineering approach to software development. A software engineer is a person who applies the principles of software engineering to design, develop, maintain, test, and evaluate computer software. The term ' ...
and quantitative analysts. The term is also sometimes used outside the finance industry to refer to those working at the intersection of
software engineering Software engineering is a systematic engineering approach to software development. A software engineer is a person who applies the principles of software engineering to design, develop, maintain, test, and evaluate computer software. The term '' ...
and quantitative research.


Mathematical and statistical approaches

Because of their backgrounds, quantitative analysts draw from various forms of mathematics:
statistics Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, indust ...
and
probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...
,
calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...
centered around partial differential equations,
linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrice ...
, discrete mathematics, and
econometrics Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. ...
. Some on the buy side may use
machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...
. 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 Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods ...
. Commonly used numerical methods are: * Finite difference method – used to solve partial differential equations; *
Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deter ...
– Also used to solve partial differential equations, but Monte Carlo simulation is also common in risk management; *
Ordinary least squares In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the ...
– used to estimate parameters in statistical regression analysis; * Spline interpolation – used to interpolate values from spot and forward interest rates curves, and volatility smiles; *
Bisection In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a ''bisector''. The most often considered types of bisectors are the ''segment bisector'' (a line that passes throug ...
, Newton, and Secant methods – used to find the
roots A root is the part of a plant, generally underground, that anchors the plant body, and absorbs and stores water and nutrients. Root or roots may also refer to: Art, entertainment, and media * ''The Root'' (magazine), an online magazine focusing ...
,
maxima and minima In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given r ...
of functions (e.g. internal rate of return, interest rate curve-building.)


Techniques

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. One of the principal mathematical tools of quantitative finance is stochastic calculus. The mindset, however, 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.


Academic and technical field journals

* Society for Industrial and Applied Mathematics (SIAM) ''Journal on Financial Mathematics'' * ''
The Journal of Portfolio Management ''The Journal of Portfolio Management'' (also known as JPM) is a quarterly academic journal for finance and investing, covering topics such as asset allocation, performance measurement, market trends, risk management, and portfolio optimization ...
'' * ''Quantitative Finance'' * ''Risk Magazine'' * ''Wilmott Magazine'' * ''Finance and Stochastics'' * ''Mathematical Finance''


Areas of work

*
Trading strategy In finance, a trading strategy is a fixed plan that is designed to achieve a profitable return by going long or short in markets. The main reasons that a properly researched trading strategy helps are its verifiability, quantifiability, consisten ...
development * Portfolio management and
Portfolio optimization Portfolio optimization is the process of selecting the best portfolio (asset distribution), out of the set of all portfolios being considered, according to some objective. The objective typically maximizes factors such as expected return, and mini ...
*
Derivatives pricing 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 u ...
and hedging: involves software development, advanced numerical techniques, and stochastic calculus. * Risk management: involves a lot of time series analysis, calibration, and backtesting. * Credit analysis *
Asset and liability management Asset and liability management (often abbreviated ALM) is the practice of managing financial risks that arise due to mismatches between the assets and liabilities as part of an investment strategy in financial accounting. ALM sits between risk ...
* Structured finance and securitization * Asset pricing


Seminal publications

* 1900 – Louis Bachelier, ''Théorie de la spéculation'' * 1938 – Frederick Macaulay, ''The Movements of Interest Rates. Bond Yields and Stock Prices in the United States since 1856'', pp. 44–53,
Bond duration In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, du ...
* 1944 –
Kiyosi Itô was a Japanese mathematician who made fundamental contributions to probability theory, in particular, the theory of stochastic processes. He invented the concept of stochastic integral and stochastic differential equation, and is known as the fo ...
, "Stochastic Integral", Proceedings of the Imperial Academy, 20(8), pp. 519–524 * 1952 – Harry Markowitz, ''Portfolio Selection'', Modern portfolio theory * 1956 –
John Kelly John or Jack Kelly may refer to: People Academics and scientists *John Kelly (engineer), Irish professor, former Registrar of University College Dublin *John Kelly (scholar) (1750–1809), at Douglas, Isle of Man * John Forrest Kelly (1859–1922) ...
, ''A New Interpretation of Information Rate'' * 1958 –
Franco Modigliani Franco Modigliani (18 June 1918 – 25 September 2003) was an Italian-American economist and the recipient of the 1985 Nobel Memorial Prize in Economics. He was a professor at University of Illinois at Urbana–Champaign, Carnegie Mellon Un ...
and Merton Miller, ''The Cost of Capital, Corporation Finance and the Theory of Investment'',
Modigliani–Miller theorem The Modigliani–Miller theorem (of Franco Modigliani, Merton Miller) is an influential element of economic theory; it forms the basis for modern thinking on capital structure. The basic theorem states that in the absence of taxes, bankruptcy cos ...
and Corporate finance * 1964 – William F. Sharpe, ''Capital asset prices: A theory of market equilibrium under conditions of risk'', Capital asset pricing model * 1965 –
John Lintner John Virgil Lintner, Jr. (February 9, 1916 – June 8, 1983) was a professor at the Harvard Business School in the 1960s and one of the co-creators (1965 a, b) of the capital asset pricing model. For a time, much confusion was created because the ...
, ''The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets'', Capital asset pricing model * 1967 – Edward O. Thorp and Sheen Kassouf, ''Beat the Market'' * 1972 – Eugene Fama and Merton Miller, ''Theory of Finance'' * 1972 – Martin L. Leibowitz and Sydney Homer, '' Inside the Yield Book'',
Fixed income analysis Fixed income analysis is the process of determining the value of a debt security based on an assessment of its risk profile, which can include interest rate risk, risk of the issuer failing to repay the debt, market supply and demand for the sec ...
* 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 Phelim P. Boyle (born 1941), is an Irish economist and distinguished professor and actuary, and a pioneer of quantitative finance. He is best known for initiating the use of Monte Carlo methods in option pricing. Biography Born on a farm ...
, ''Options: A Monte Carlo Approach'', Monte Carlo methods for option pricing * 1977 – Oldřich Vašíček, ''An equilibrium characterisation of the term structure'',
Vasicek model In finance, the Vasicek model is a mathematical model describing the evolution of interest rates. It is a type of one-factor short-rate model as it describes interest rate movements as driven by only one source of market risk. The model can be use ...
* 1979 –
John Carrington Cox John Carrington Cox is the Nomura Professor of Finance at the MIT Sloan School of Management. He is one of the world's leading experts on options theory and one of the inventors of the Cox–Ross–Rubinstein model for option pricing, as well ...
; Stephen Ross; Mark Rubinstein, ''Option pricing: A simplified approach'',
Binomial options pricing model In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" ( lattice based) model of the varying price over time of the underlying f ...
and Lattice 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 In mathematical finance, the Cox–Ingersoll–Ross (CIR) model describes the evolution of interest rates. It is a type of "one factor model" ( short-rate model) as it describes interest rate movements as driven by only one source of mark ...
* 1987 – Giovanni Barone-Adesi and
Robert Whaley Robert Antawon Whaley (born April 16, 1982) is an American former professional basketball player. High school and college career Whaley graduated from Benton Harbor High School in 2001. He was a leading contender for Mr. Basketball of Michigan, ...
, ''Efficient analytic approximation of American option values''. Journal of Finance. 42 (2): 301–20. Barone-Adesi and Whaley method for pricing American options. * 1987 – David Heath, Robert A. Jarrow, and Andrew Morton ''Bond pricing and the term structure of interest rates: a new methodology'' (1987), Heath–Jarrow–Morton framework for interest rates * 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 In mathematical finance, the Black–Derman–Toy model (BDT) is a popular short-rate model used in the pricing of bond options, swaptions and other interest rate derivatives; see . It is a one-factor model; that is, a single stochastic factor—t ...
* 1990 – John Hull and Alan White, "Pricing interest-rate derivative securities", The Review of Financial Studies, Vol 3, No. 4 (1990) Hull-White model * 1991 – Ioannis Karatzas & Steven E. Shreve. ''Brownian motion and stochastic calculus''. * 1992 – Fischer Black and Robert Litterman: Global Portfolio Optimization, Financial Analysts Journal, September 1992, pp. 28–43 Black–Litterman model * 1994 –
J.P. Morgan JP may refer to: Arts and media * ''JP'' (album), 2001, by American singer Jesse Powell * ''Jp'' (magazine), an American Jeep magazine * ''Jönköpings-Posten'', a Swedish newspaper * Judas Priest, an English heavy metal band * ''Jurassic Par ...
RiskMetrics Group
RiskMetrics Technical Document
1996, RiskMetrics model and framework * 2002 – Patrick Hagan, Deep Kumar, Andrew Lesniewski, Diana Woodward, ''Managing Smile Risk'', Wilmott Magazine, January 2002, SABR volatility model. * 2004 – Emanuel Derman, ''My Life as a Quant: Reflections on Physics and Finance''


See also

*
List of quantitative analysts This is a list of ''notable'' quantitative analysts (by ''surname''); see also § Seminal publications there, and List of financial economists. Pioneers * Kenneth Arrow, (1921 – 2017), American economist, Social choice theory. * Louis Bacheli ...
*
Quantitative fund A quantitative fund is an investment fund that uses quantitative investment management instead of fundamental human analysis. Investment process :''See for a listing of relevant articles.'' An investment process is classified as quantitative w ...
* Financial modeling *
Black–Scholes equation In mathematical finance, the Black–Scholes equation is a partial differential equation (PDE) governing the price evolution of a European call or European put under the Black–Scholes model. Broadly speaking, the term may refer to a similar PDE ...
* Financial signal processing *
Financial analyst A financial analyst is a professional, undertaking financial analysis for external or internal clients as a core feature of the job. The role may specifically be titled securities analyst, research analyst, equity analyst, investment analyst, ...
* Technical analysis * Fundamental analysis *
Financial economics Financial economics, also known as finance, is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on ''both sides'' of a trade". William F. Sharpe"Financia ...
* Mathematical finance * Alpha generation platform


References


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'' * Patterson, Scott D. (2010). ''
The Quants ''The Quants'' is the debut New York Times best selling book by Wall Street journalist Scott Patterson. It was released on February 2, 2010 by Crown Business. The book describes the world of quantitative analysis and the various hedge funds t ...
: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It''. Crown Business, 352 pages.
Amazon page for book
vi
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''. * Read, Colin (2012) ''Rise of the Quants'' (Great Minds in Finance Series)
Analysing Quantitative Data for Business and Management Students


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://qwafafew.org/ – QWAFAFEW – Quantitative Work Alliance for Finance Education and Wisdom * http://prmia.org – PRMIA—Professional Risk Managers Industry Association * http://iaqf.org – International Association of Quantitative Finance * http://www.lqg.org.uk/ – London Quant Group * http://quant.stackexchange.com – question and answer site for quantitative finance {{stock market Valuation (finance) Mathematical finance Financial analysts