A master's degree in quantitative finance concerns the application of mathematical methods to the solution of problems in

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 ...

. There are several like-titled degrees which may further focus on

financial engineering Financial engineering is a multidisciplinary field involving financial theory, methods of engineering, tools of mathematics and the practice of programming. It has also been defined as the application of technical methods, especially from mathem ...

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.,%20Spring ...

, mathematical finance, and/or financial risk management. In general, these degrees aim to prepare students for roles as "quants" (

quantitative analyst Quantitative may refer to: * Quantitative research, scientific investigation of quantitative properties * Quantitative analysis (disambiguation) * Quantitative verse, a metrical system in poetry * Statistics, also known as quantitative analysis ...

s), including

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

, structuring,

trading Trade involves the transfer of goods and services from one person or entity to another, often in exchange for money. Economists refer to a system or network that allows trade as a market. An early form of trade, barter, saw the direct excha ...

, and

investing Investment is the dedication of money to purchase of an asset to attain an increase in value over a period of time. Investment requires a sacrifice of some present asset, such as time, money, or effort. In finance, the purpose of investing i ...

; in particular, these degrees emphasize derivatives and fixed income, and the hedging and

management Management (or managing) is the administration of an organization, whether it is a business, a nonprofit organization, or a Government agency, government body. It is the art and science of managing resources of the business. Management includ ...

of the resultant

market Market is a term used to describe concepts such as: *Market (economics), system in which parties engage in transactions according to supply and demand *Market economy *Marketplace, a physical marketplace or public market Geography *Märket, an ...

and

credit risk A credit risk is risk of default on a debt that may arise from a borrower failing to make required payments. In the first resort, the risk is that of the lender and includes lost principal and interest, disruption to cash flows, and increased ...

. Formal master's-level training in

quantitative finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require ...

has existed since 1990.

Structure

The program is usually one to one and a half years in duration, and may include a

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: ...

component. Entrance requirements are generally

multivariable calculus Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving several variables, rather ...

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 matrices ...

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

s and some exposure to

computer programming Computer programming is the process of performing a particular computation (or more generally, accomplishing a specific computing result), usually by designing and building an executable computer program. Programming involves tasks such as anal ...

(usually

C++ C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded significan ...

); programs emphasizing

financial mathematics Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require ...

may require some background in measure theory. Initially, the

curriculum In education, a curriculum (; : curricula or curriculums) is broadly defined as the totality of student experiences that occur in the educational process. The term often refers specifically to a planned sequence of instruction, or to a view ...

builds quantitative skills, and simultaneously develops the underlying finance theory: *The quantitative component draws on

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 ...

computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...

and statistical modelling, and emphasizes

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. This field was created an ...

numerical methods 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 th ...

and simulation techniques; see . Some programs also focus on

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. 8 ...

time series analysis In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in m ...

. *The theory component usually includes a formal study of

, addressing asset pricing and

financial markets A financial market is a market in which people trade financial securities and derivatives at low transaction costs. Some of the securities include stocks and bonds, raw materials and precious metals, which are known in the financial ma ...

; some programs may also include general coverage of

economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes ...

, accounting, corporate finance and portfolio management. The components are then integrated, addressing the modelling, valuation and hedging of

equity derivative In finance, an equity derivative is a class of derivatives whose value is at least partly ''derived'' from one or more underlying equity securities. Options and futures are by far the most common equity derivatives, however there are many other ty ...

s, commodity derivatives,

foreign exchange derivative A foreign exchange derivative is a financial derivative whose payoff depends on the foreign exchange rates of two (or more) currencies. These instruments are commonly used for currency speculation and arbitrage or for hedging foreign exchange r ...

s, and fixed income instruments and their related credit- and

interest rate derivative In finance, an interest rate derivative (IRD) is a derivative whose payments are determined through calculation techniques where the underlying benchmark product is an interest rate, or set of different interest rates. There are a multitude of diff ...

s; see . Programs often include dedicated modules in

market risk Market risk is the risk of losses in positions arising from movements in market variables like prices and volatility. There is no unique classification as each classification may refer to different aspects of market risk. Nevertheless, the most ...

and

, with some degrees offered as specialized “Masters in Financial Risk Management”; the techniques covered are

value at risk Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by ...

, stress testing, and "sensitivities" analysis, and in parallel, the Basel capital / liquidity requirements. Increasingly, programs include quantitative portfolio management and -optimization; see and § Portfolio theory. Recently, topics (or specializations) in 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 ...

are becoming common. The title of the degree will depend on emphasis, the major differences between programs being the curriculum's distribution between mathematical theory, quantitative techniques and financial applications. The more theoretically oriented degrees are usually termed " Master's in Mathematical Finance" or " Master's in Financial Mathematics" while those oriented toward practice are termed " Master's in Financial Engineering" (MFE or MSFE), " Master's in Computational Finance" (MCF or MSCF), or sometimes simply " Master's in Finance" (MFin). "Master's in Quantitative Finance" is the more general degree title, although "MQF" degrees are often less theoretical and more practical. The practice oriented programs are often positioned as

professional degree A professional degree, formerly known in the US as a first professional degree, is a degree that prepares someone to work in a particular profession, practice, or industry sector often meeting the academic requirements for licensure or accreditatio ...

s (and in the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territori ...

, are sometimes offered as Professional Science Master's). Programs are sometimes offered as a

Master of Engineering A Master of Engineering (abbreviated MEng, M.E. or M.Eng.) is either an academic or professional master's degree in the field of engineering. International variations Australia In Australia, the Master of Engineering degree is a research de ...

, or as a Master of

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 ...

Comparison with other qualifications

The program differs from a Master of Science in Finance (MSF), and an MBA in finance, in that these degrees aim to produce finance generalists as opposed to "quants", and therefore focus on corporate finance, accounting,

equity valuation In financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit fr ...

and portfolio management. The treatment of any common topics—usually " derivatives",

financial modeling Financial modeling is the task of building an abstract representation (a model) of a real world financial situation. This is a mathematical model designed to represent (a simplified version of) the performance of a financial asset or portfolio ...

, and risk management—will be less (or even non) technical. Entrance requirements are similarly less mathematical. Note that

Master of Finance The Master of Finance is a master's degree awarded by universities or graduate schools preparing students for careers in finance. The degree is often titled Master in Finance (M.Fin., MiF, MFin), or Master of Science in Finance (MSF in North Am ...

(M.Fin.) and MSc. in Finance degrees, as distinct from the MSF, may be substantially similar to the MQF. There is some overlap with degrees in actuarial science, and both degrees are occasionally offered by the same department. Nevertheless, the programs are almost always separate and distinct. Specifically, whereas actuarial programs cover risk and uncertainty as applied to pensions,

insurance Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge ...

and investments, quantitative finance programs are broader (although offer less depth in these areas), and prepare graduates for various of the highly numerate roles in finance and for other areas that require "quants". There is similarly overlap with a

Master of Financial Economics A master's degree in Financial Economics provides a rigorous understanding of theoretical finance and the economic framework upon which that theory is based. The degree is postgraduate, and usually incorporates a thesis or research component. Progr ...

, although the emphasis is very different. That degree focuses on the underlying economics, and on developing and testing theoretical models, and aims to prepare graduates for

research Research is " creative and systematic work undertaken to increase the stock of knowledge". It involves the collection, organization and analysis of evidence to increase understanding of a topic, characterized by a particular attentiveness ...

based roles and for doctoral study. The curriculum therefore emphasises coverage of financial theory, and of

, while the treatment of model ''implementation'' (through mathematical modeling and programming), while important, is secondary. Entrance requirements are similarly less mathematical. Some Financial Economics degrees are substantially quantitative, and are largely akin to the MQF. For students whose interests in finance are commercial rather than

academic An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary or tertiary higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosophy, ...

, a Master's in Quantitative Finance may be seen as an alternative to a PhD in finance. At the same time though, "Master's in Mathematical Finance" programs are often positioned as providing a basis for doctoral study.

History

The first quantitative finance master's programs in the US were offered by

Illinois Institute of Technology Illinois Institute of Technology (IIT) is a private research university in Chicago, Illinois. Tracing its history to 1890, the present name was adopted upon the merger of the Armour Institute and Lewis Institute in 1940. The university has prog ...

in 1990, under Dr. Michael Ong. The programs offered were the "Master of Science in Quantitative Finance" and "Master of Science in Financial Markets and Trading", and were combined in 2008 to become the "Master of Science in Finance, with Financial Engineering Concentration". The NYU-Poly Financial Engineering degree was the second program of its kind, and the first to be certified by the

International Association of Financial Engineers The International Association for Quantitative Finance (IAQF), formerly the International Association of Financial Engineers (IAFE), is a non-profit professional society dedicated to fostering the fields of quantitative finance and financial engin ...

Carnegie Mellon Carnegie may refer to: People *Carnegie (surname), including a list of people with the name *Clan Carnegie, a lowland Scottish clan Institutions Named for Andrew Carnegie * Carnegie Building (Troy, New York), on the campus of Rensselaer Polyte ...

introduced its "Master of Computational Finance" program in 1994.

OGI Ogi may refer to: People * Adolf Ogi (born 1942), Swiss politician *, Japanese football player *, Japanese actress and politician *Darko Ostojić (born 1965), nicknamed Ogi, Bosnian musician and actor *, Japanese football player *Ogi Ogas (born 19 ...

's Computational Finance Program (1996, now discontinued) was the first such program based in a

department. Other pioneering programs include those at NYU's Courant Institute, Columbia,

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ni ...

Cornell Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach a ...

UCLA The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California ...

, DePaul and

MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...

. Subsequent growth in the number and location of programs has paralleled the growth of

—with its growing importance across all aspects of the financial services industries—and of risk management as

profession A profession is a field of work that has been successfully ''professionalized''. It can be defined as a disciplined group of individuals, '' professionals'', who adhere to ethical standards and who hold themselves out as, and are accepted by ...

s. Programs are now widely offered internationally—see links below—and in some cases are available

online In computer technology and telecommunications, online indicates a state of connectivity and offline indicates a disconnected state. In modern terminology, this usually refers to an Internet connection, but (especially when expressed "on line" o ...

or via

distance education Distance education, also known as distance learning, is the education of students who may not always be physically present at a school, or where the learner and the teacher are separated in both time and distance. Traditionally, this usually in ...

(e.g.

Washington Washington commonly refers to: * Washington (state), United States * Washington, D.C., the capital of the United States ** A metonym for the federal government of the United States ** Washington metropolitan area, the metropolitan area centered o ...

York York is a cathedral city with Roman origins, sited at the confluence of the rivers Ouse and Foss in North Yorkshire, England. It is the historic county town of Yorkshire. The city has many historic buildings and other structures, such as a ...

, Stevens, USC,

NUS NUS or Nus may refer to: * National University of Singapore * Nus, a town in the Aosta Valley of Italy * Neglected and Underutilized Species, or Neglected and Underutilized Crops * National Union of Students (Australia) * National Union of Students ...

, TU Kaiserslautern,). In a few cases, a quantitative-finance

MBA A Master of Business Administration (MBA; also Master's in Business Administration) is a postgraduate degree focused on business administration. The core courses in an MBA program cover various areas of business administration such as accounti ...

-specialization is offered. More recently

undergraduate Undergraduate education is education conducted after secondary education and before postgraduate education. It typically includes all postsecondary programs up to the level of a bachelor's degree. For example, in the United States, an entry-le ...

programs are available, both in the US (e.g. Ball State, James Madison, McIntire.) and internationally (e.g.

Essex Essex () is a county in the East of England. One of the home counties, it borders Suffolk and Cambridgeshire to the north, the North Sea to the east, Hertfordshire to the west, Kent across the estuary of the River Thames to the south, and Grea ...

HKUST The Hong Kong University of Science and Technology (HKUST) is a public research university in Clear Water Bay Peninsula, New Territories, Hong Kong. Founded in 1991 by the British Hong Kong Government, it was the territory's third institution ...

UNISA The University of South Australia (UniSA) is a public research university in the Australian state of South Australia. It is a founding member of the Australian Technology Network of universities, and is the largest university in South Australi ...

References

External links

Financial Engineering Core Body of Knowledge

International Association for Quantitative Finance The International Association for Quantitative Finance (IAQF), formerly the International Association of Financial Engineers (IAFE), is a non-profit professional society dedicated to fostering the fields of quantitative finance and financial engin ...

Listing of academic programs in financial engineering/financial mathematics
International Association for Quantitative Finance {{Academic degrees Quantitative Finance, Master Mathematical finance Business qualifications

Structure

Comparison with other qualifications

History

See also

References

External links