A master's degree in quantitative finance is a
postgraduate degree focused on the application of
mathematical methods to the solution of problems in
financial economics
Financial economics 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"Financial Economics", in
Its co ...
.
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 mathe ...
,
computational finance
Computational finance is a branch of applied computer science that deals with problems of practical interest in finance.Rüdiger U. Seydel, ''Tools for Computational Finance'', Springer; 3rd edition (May 11, 2006) 978-3540279235 Some slightly diff ...
,
mathematical finance
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field.
In general, there exist two separate branches of finance that req ...
, and/or
financial risk management
Financial risk management is the practice of protecting Value (economics), economic value in a business, firm by managing exposure to financial risk - principally credit risk and market risk, with more specific variants as listed aside - as well ...
.
In general, these degrees aim to prepare students for roles as "quants" (
quantitative analysts); in particular, these degrees emphasize
derivatives and
fixed income
Fixed income refers to any type of investment under which the borrower or issuer is obliged to make payments of a fixed amount on a fixed schedule. For example, the borrower may have to pay interest at a fixed rate once a year and repay the pr ...
, and the
hedging and
management
Management (or managing) is the administration of organizations, whether businesses, nonprofit organizations, or a Government agency, government bodies through business administration, Nonprofit studies, nonprofit management, or the political s ...
of the resultant
market and
credit risk
Credit risk is the chance that a borrower does not repay a loan
In finance, a loan is the tender of money by one party to another with an agreement to pay it back. The recipient, or borrower, incurs a debt and is usually required to pay ...
.
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 in the financial field.
In general, there exist two separate branches of finance that requ ...
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: D ...
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 multiple variables ('' mult ...
,
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 matrix (mathemat ...
,
differential equations and some exposure to
computer programming
Computer programming or coding is the composition of sequences of instructions, called computer program, programs, that computers can follow to perform tasks. It involves designing and implementing algorithms, step-by-step specifications of proc ...
(usually
C++);
programs emphasizing
financial mathematics
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the Finance#Quantitative_finance, financial field.
In general, there exist two separate ...
may require some background in
measure theory
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude (mathematics), magnitude, mass, and probability of events. These seemingl ...
.
Initially, the
curriculum
In education, a curriculum (; : curriculums or curricula ) is the totality of student experiences that occur in an educational process. The term often refers specifically to a planned sequence of instruction, or to a view of the student's experi ...
builds quantitative skills, and simultaneously develops the underlying finance theory:
*The quantitative component draws on
applied mathematics
Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...
,
computer science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...
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 t ...
and
simulation techniques;
see . Some programs also focus on
econometrics
Econometrics is an 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, 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. ...
.
*The theory component usually includes a formal study of
financial economics
Financial economics 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"Financial Economics", in
Its co ...
, addressing
asset pricing
In financial economics, asset pricing refers to a formal treatment and development of two interrelated Price, pricing principles, outlined below, together with the resultant models. There have been many models developed for different situations, ...
and
financial markets; some programs may also include general coverage of
economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interac ...
,
accounting
Accounting, also known as accountancy, is the process of recording and processing information about economic entity, economic entities, such as businesses and corporations. Accounting measures the results of an organization's economic activit ...
,
corporate finance
Corporate finance is an area of finance that deals with the sources of funding, and the capital structure of businesses, the actions that managers take to increase the Value investing, value of the firm to the shareholders, and the tools and analy ...
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 Derivative (finance), derivatives whose value is at least partly ''derived'' from one or more underlying stock, equity securities. Option (finance), Options and Future (finance), futures are by far the ...
s,
commodity derivatives,
foreign exchange derivatives, 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 dif ...
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 m ...
and
credit risk
Credit risk is the chance that a borrower does not repay a loan
In finance, a loan is the tender of money by one party to another with an agreement to pay it back. The recipient, or borrower, incurs a debt and is usually required to pay ...
, with some degrees offered as specialized “Masters in
Financial Risk Management
Financial risk management is the practice of protecting Value (economics), economic value in a business, firm by managing exposure to financial risk - principally credit risk and market risk, with more specific variants as listed aside - as well ...
”;
the techniques covered are
value at risk,
stress testing
Stress testing is a form of deliberately intense or thorough testing, used to determine the stability of a given system, critical infrastructure or entity. It involves testing beyond normal operational capacity, often to a breaking point, in orde ...
, 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
Data science is an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processing, scientific visualization, algorithms and systems to extract or extrapolate knowledge from potentially noisy, stru ...
and
machine learning
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task ( ...
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 degrees (and in the
United States
The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...
, are sometimes offered as
Professional Science Master's). Programs are sometimes offered as a
Master of Engineering,
or as a Master of
Operations Research
Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and ...
.
Comparison with other qualifications
The program differs from a
Master of Science in Finance
Master, master's or masters may refer to:
Ranks or titles
In education:
*Master (college), head of a college
*Master's degree, a postgraduate or sometimes undergraduate degree in the specified discipline
* Schoolmaster or master, presiding offic ...
(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
Corporate finance is an area of finance that deals with the sources of funding, and the capital structure of businesses, the actions that managers take to increase the Value investing, value of the firm to the shareholders, and the tools and analy ...
,
accounting
Accounting, also known as accountancy, is the process of recording and processing information about economic entity, economic entities, such as businesses and corporations. Accounting measures the results of an organization's economic activit ...
,
equity valuation 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 o ...
, and
risk management
Risk management is the identification, evaluation, and prioritization of risks, followed by the minimization, monitoring, and control of the impact or probability of those risks occurring. Risks can come from various sources (i.e, Threat (sec ...
—will be less (or even non) technical. Entrance requirements are similarly less mathematical. Note that
Master of Finance (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
Actuarial science is the discipline that applies mathematics, mathematical and statistics, statistical methods to Risk assessment, assess risk in insurance, pension, finance, investment and other industries and professions.
Actuary, Actuaries a ...
,
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
pension
A pension (; ) is a fund into which amounts are paid regularly during an individual's working career, and from which periodic payments are made to support the person's retirement from work. A pension may be either a " defined benefit plan", wh ...
s,
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 protect ...
and
investment
Investment is traditionally defined as the "commitment of resources into something expected to gain value over time". If an investment involves money, then it can be defined as a "commitment of money to receive more money later". From a broade ...
s, 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, 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 to ...
based roles and for
doctoral study. The curriculum therefore emphasises coverage of financial theory, and of
econometrics
Econometrics is an 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 ...
, 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 tertiary education. The name traces back to Plato's school of philosophy, founded approximately 386 BC at Akademia, a sanctuary of Athena, the go ...
, 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
In 1989
Cornell University's Operations Research and Information Engineering department hosted the first ever academic meeting to focus on financial engineering, which led to the development of the first research journal in the field, ''Mathematical Finance''. The first quantitative finance master's programs in the US were offered by
Illinois Institute of Technology
The Illinois Institute of Technology, commonly referred to as Illinois Tech and IIT, is a Private university, private research university in Chicago, Illinois, United States. Tracing its history to 1890, the present name was adopted upon the m ...
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.
Carnegie Mellon introduced its "Master of Computational Finance" program in 1994.
OGI's Computational Finance Program (1996, now discontinued) was the first such program based in a
computer science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...
department.
Other pioneering programs include those at
NYU's Courant Institute,
Columbia,
Princeton,
Cornell,
UCLA
The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California, United States. Its academic roots were established in 1881 as a normal school then known as the southern branch of the C ...
,
DePaul and
MIT. The program in Quantitative Finance is also popular in the
DACH region with renowned programs at
Vienna University of Economics and Business,
ETH Zurich
ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ran ...
(together with
University of Zurich
The University of Zurich (UZH, ) is a public university, public research university in Zurich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 from the existing colleges of the ...
), and
University of St. Gallen.
Subsequent growth in the number and location of programs has paralleled the growth of
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 mathe ...
—with its growing importance across all aspects of the financial services industries—and of
risk management
Risk management is the identification, evaluation, and prioritization of risks, followed by the minimization, monitoring, and control of the impact or probability of those risks occurring. Risks can come from various sources (i.e, Threat (sec ...
as
profession
A profession is a field of Work (human activity), 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 ...
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 as "on lin ...
or via
distance education
(e.g.
Washington,
York
York is a cathedral city in North Yorkshire, England, with Roman Britain, Roman origins, sited at the confluence of the rivers River Ouse, Yorkshire, Ouse and River Foss, Foss. It has many historic buildings and other structures, such as a Yor ...
,
Stevens,
USC USC may refer to:
Education
United States
* Universidad del Sagrado Corazón, Santurce, Puerto Rico
* University of South Carolina, Columbia, South Carolina
** University of South Carolina System, a state university system of South Carolina
* ...
,
NUS,
TU Kaiserslautern,).
In a few cases, a quantitative-finance
MBA-specialization is offered.
More recently
undergraduate
Undergraduate education is education conducted after secondary education and before postgraduate education, usually in a college or university. It typically includes all postsecondary programs up to the level of a bachelor's degree. For example, ...
programs are available, both in the US
(e.g.
Ball State,
James Madison,
McIntire.)
and internationally
(e.g.
Essex
Essex ( ) is a Ceremonial counties of England, ceremonial county in the East of England, and one of the home counties. It is bordered by Cambridgeshire and Suffolk to the north, the North Sea to the east, Kent across the Thames Estuary to the ...
,
HKUST,
UNISA).
See also
*
Certificate in Quantitative Finance
*
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 o ...
*
List of quantitative analysts
*
Master of Finance
*
Master of Financial Economics
*
Mathematical finance
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field.
In general, there exist two separate branches of finance that req ...
*
QEM
*
Quantitative analyst
*Context:
**
**
**
References
External links
Financial Engineering Core Body of Knowledge International Association for Quantitative FinanceListing of academic programs in financial engineering/financial mathematics International Association for Quantitative Finance
{{Academic degrees
Quantitative Finance, Master
Mathematical finance
Business qualifications