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**Financial engineering** is a multidisciplinary field involving financial theory, methods of engineering, tools of mathematics and the practice of programming.^{ [1] } It has also been defined as the application of technical methods, especially from mathematical finance and computational finance, in the practice of finance.^{ [2] }

**Engineering** is the use of scientific principles to design and build machines, structures, and other things, including bridges, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specialized fields of engineering, each with a more specific emphasis on particular areas of applied mathematics, applied science, and types of application. See glossary of engineering.

**Mathematics** includes the study of such topics as quantity, structure (algebra), space (geometry), and change. It has no generally accepted definition.

**Mathematical finance**, also known as **quantitative finance** and **financial mathematics**, is a field of applied mathematics, concerned with mathematical modeling of financial markets. Generally, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. Thus, for example, while a financial economist might study the structural reasons why a company may have a certain share price, a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the corresponding value of derivatives of the stock. The fundamental theorem of arbitrage-free pricing is one of the key theorems in mathematical finance, while the Black–Scholes equation and formula are amongst the key results.

It is generally (but not always) a disparaging term, implying that someone is profiting from paper games at the expense of employees and investors.^{ [3] }

Financial engineering draws on tools from applied mathematics, computer science, statistics and economic theory.^{ [4] } In the broadest sense, anyone who uses technical tools in finance could be called a financial engineer, for example any computer programmer in a bank or any statistician in a government economic bureau.^{ [5] } However, most practitioners restrict the term to someone educated in the full range of tools of modern finance and whose work is informed by financial theory.^{ [6] } It is sometimes restricted even further, to cover only those originating new financial products and strategies.^{ [7] }

**Applied mathematics** is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics.

**Computer science** is the study of processes that interact with data and that can be represented as data in the form of programs. It enables the use of algorithms to manipulate, store, and communicate digital information. A computer scientist studies the theory of computation and the practice of designing software systems.

**Statistics** is the discipline that concerns the collection, organization, displaying, analysis, interpretation and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments. See glossary of probability and statistics.

Despite its name, financial engineering does not belong to any of the fields in traditional professional engineering even though many financial engineers have studied engineering beforehand and many universities offering a postgraduate degree in this field require applicants to have a background in engineering as well.^{ [8] } In the United States, the Accreditation Board for Engineering and Technology (ABET) does not accredit financial engineering degrees.^{ [9] } In the United States, financial engineering programs are accredited by the *International Association of Quantitative Finance*.^{ [10] }

An older use of the term "financial engineering" that is less common today is aggressive restructuring of corporate balance sheets.

In financial accounting, a **balance sheet ** or **statement of financial position** or **statement of financial condition** is a summary of the financial balances of an individual or organization, whether it be a sole proprietorship, a business partnership, a corporation, private limited company or other organization such as Government or not-for-profit entity. Assets, liabilities and ownership equity are listed as of a specific date, such as the end of its financial year. A balance sheet is often described as a "snapshot of a company's financial condition". Of the four basic financial statements, the balance sheet is the only statement which applies to a single point in time of a business' calendar year.

Financial engineering plays a key role in the customer-driven derivatives business^{ [11] } which encompasses quantitative modelling and programming, trading and risk managing derivative products in compliance with the regulations and Basel capital/liquidity requirements.

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

Quantitative analyst ("Quant") is a broad term that covers any person who uses math for practical purposes, including financial engineers. Quant is often taken to mean “financial quant,” in which case it is similar to financial engineer.^{ [12] } The difference is that it is possible to be a theoretical quant, or a quant in only one specialized niche in finance, while “financial engineer” usually implies a practitioner with broad expertise.^{ [13] }

“Rocket scientist” (aerospace engineer) is an older term, first coined in the development of rockets in WWII (Wernher von Braun), and later, the NASA space program; it was adapted by the first generation of financial quants who arrived on Wall Street in the late 1970s and early 1980s.^{ [14] } While basically synonymous with financial engineer, it implies adventurousness and fondness for disruptive innovation.^{ [15] } Financial "Rocket scientists" were usually trained in applied mathematics, statistics or finance; and spent their entire careers in risk-taking.^{ [16] } They were not hired for their mathematical talents, they either worked for themselves or applied mathematical techniques to traditional financial jobs.^{ [6] }^{ [15] } The later generation of financial engineers were more likely to have PhDs in mathematics or physics and often started their careers in academics or non-financial fields.^{ [17] }

Mathematical finance is the application of mathematics to finance.^{ [7] } Computational finance and mathematical finance are both subfields of financial engineering. Computational finance is a field in computer science and deals with the data and algorithms that arise in financial modeling.

The first degree programs in financial engineering were set up in the early 1990s. The number and size of programs has grown rapidly, so now some people use the term “financial engineer” to mean someone who has a degree in the field.^{ [4] } The financial engineering program at New York University Polytechnic School of Engineering was the first curriculum to be certified by the International Association of Financial Engineers.^{ [18] }^{ [19] }

The main applications of financial engineering^{ [20] }^{ [21] } are to:

*See also: Financial mathematics#Criticism; Financial economics#Challenges and criticism.*

One of the critics of financial engineering is Nassim Taleb, a professor of financial engineering at Polytechnic Institute of New York University ^{ [22] } who argues that it replaces common sense and leads to disaster. A series of economic collapses has led many governments to argue a return to "real" engineering from financial engineering.

Many other authors have identified specific problems in financial engineering that caused catastrophes: Aaron Brown ^{ [23] } named confusion between quants and regulators over the meaning of “capital”, Felix Salmon ^{ [24] } gently pointed to the Gaussian copula, Ian Stewart^{ [25] } criticized the Black-Scholes formula, Pablo Triana^{ [26] } dislikes value at risk and Scott Patterson ^{ [27] }^{ [28] } accused quantitative traders and later high-frequency traders.

A gentler criticism came from Emanuel Derman ^{ [29] } who heads a financial engineering degree program at Columbia University. He blames over-reliance on models for financial problems.

The financial innovation often associated with financial engineers was mocked by former chairman of the Federal Reserve Paul Volcker in 2009 when he said it was a code word for risky securities, that brought no benefits to society. For most people, he said, the advent of the ATM was more crucial than any asset-backed bond.^{ [30] }

Beder, Tanya S.; Marshall, Cara M. (2011). *Financial Engineering: The Evolution of a Profession*. John Wiley & Sons.

A **quantitative analyst** is a person who specializes in the application of mathematical and statistical methods to financial and risk management problems. The occupation is similar to those in industrial mathematics in other industries.

**Financial modeling** is the task of building an abstract representation of a real world financial situation. This is a mathematical model designed to represent the performance of a financial asset or portfolio of a business, project, or any other investment.

**Computational finance** is a branch of applied computer science that deals with problems of practical interest in finance. Some slightly different definitions are the study of data and algorithms currently used in finance and the mathematics of computer programs that realize financial models or systems.

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 Lattice model (finance) #Interest rate derivatives. It is a one-factor model; that is, a single stochastic factor—the short rate—determines the future evolution of all interest rates. It was the first model to combine the mean-reverting behaviour of the short rate with the lognormal distribution, and is still widely used.

**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*.

In finance, a **lattice model** is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date. For interest rate derivatives lattices are additionally useful in that they address many of the issues encountered with continuous models, such as pull to par. The method is also used for valuing certain exotic options, where because of path dependence in the payoff, Monte Carlo methods for option pricing fail to account for optimal decisions to terminate the derivative by early exercise., though methods now exist for solving this problem.

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 finance.

**Jim Gatheral** is a researcher in the field of mathematical finance, who has contributed to the study of volatility as applied to the pricing and risk management of derivatives. A recurrent subject in his books and papers is the volatility smile, and he published in 2006 a book *The Volatility Surface* based on a course he taught for six years at New York University, along with Nassim Taleb. More recently his work has moved in the direction of market microstructure, especially as applied to algorithmic trading. He is the author of *The Volatility Surface: A Practitioner's Guide.*

**Neil A. Chriss** is a mathematician, academic, hedge fund manager, philanthropist and a founding board member of the charity organization "Math for America" which seeks to improve math education in the United States. Chriss also serves on the board of trustees of the Institute for Advanced Study.

**Paul Wilmott** is an English researcher, consultant and lecturer in quantitative finance. He is best known as the author of various academic and practitioner texts on risk and derivatives, for *Wilmott* magazine and Wilmott.com, a quantitative finance portal, and for his prescient warnings about the misuse of mathematics in finance.

**Aaron C. Brown** is an American finance practitioner, well known as an author on risk management and gambling-related issues. He also speaks frequently at professional and academic conferences. He was Chief Risk Manager at AQR Capital Management. He was one of the original developers of value at risk and one of its strongest proponents.

**Bruno Dupire** is a researcher and lecturer in quantitative finance. He is currently Head of Quantitative Research at Bloomberg LP. He is best known for his contributions to local volatility modeling and Functional Ito Calculus. He is also an Instructor at New York University since 2005, in the Courant Master of Science Program in Mathematics in Finance.

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 other than financial securities valuation, such as assigning consumer credit scores, real-time probability prediction of fraudulent credit card transactions, and computing the probability of air flight passenger being a terrorist. Rebonato in 2002 defines model risk as "the risk of occurrence of a significant difference between the mark-to-model value of a complex and/or illiquid instrument, and the price at which the same instrument is revealed to have traded in the market".

The **Financial Modelers' Manifesto** was a proposal for more responsibility in risk management and quantitative finance written by financial engineers Emanuel Derman and Paul Wilmott. The manifesto includes a Modelers' Hippocratic Oath. The structure of the Financial Modelers' Manifesto mirrors that of *The Communist Manifesto* of 1848.

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. Programs may be offered jointly by the business school and the economics department.

**Mark Suresh Joshi** was a researcher and consultant in mathematical finance, and a Professor at the University of Melbourne. His research focused on derivatives pricing and interest rate derivatives in particular. He is the author of numerous research articles and seven books; his popular guides, "On becoming a quant" and "How to Get a Quant Job in Finance", are widely read.

**Piotr Karasinski** is a pioneering quantitative analyst, best known for the Black–Karasinski short rate model which he co-developed with the late Fischer Black. His contributions to quantitative finance include models for interest rates, equity and hybrid products and random volatility.

**"Rocket science" in finance** is a metaphor for activity carried out by specialised quantitative staff to provide detailed output from mathematical modeling and computational simulations to support investment decisions. Their work depends on use of complex mathematical models implemented in sophisticated IT environments.

- ↑ "MS in Financial Engineering". Columbia University Department of Industrial Engineering and Operations Research. Archived from the original on 2017-01-19. Retrieved 2017-01-18.
- ↑ Tanya S. Beder and Cara M. Marshall,
*Financial Engineering: The Evolution of a Profession*, Wiley (June 7, 2011) 978-0470455814 - ↑ Michael Pomerleano and William Shaw (editors),
*Corporate Restructuring: Lessons from Experience*, World Bank Publications (April 2005) 978-0821359280 - 1 2 "What is Financial Engineering?". International Association of Financial Engineers. Archived from the original on 2012-06-30. Retrieved 2012-07-22.
- ↑ Ali N. Akansu and Mustafa U. Torun. (2015), A Primer for Financial Engineering: Financial Signal Processing and Electronic Trading, Boston, MA: Academic Press, ISBN 978-0-12-801561-2
- 1 2 Salih N. Neftci,
*Principles of Financial Engineering*, Academic Press (December 15, 2008) 978-0123735744 - 1 2 Robert Dubil,
*Financial Engineering and Arbitrage in the Financial Markets*, Wiley (October 11, 2011) 978-0470746011 - ↑ Entry requirements | Imperial College Business School. 2016. Entry requirements | Imperial College Business School. [ONLINE] Available at: http://wwwf.imperial.ac.uk/business-school/programmes/msc-risk-management/entry-requirements/ Archived 2016-06-27 at the Wayback Machine . [Accessed 30 June 2016]. Add to My References
- ↑ "List of Member Societies". ABET. Archived from the original on 2013-04-30. Retrieved 26 April 2013.
- ↑ "{title}". Archived from the original on 2018-06-13. Retrieved 2018-08-21.
- ↑ Qu, Dong (2016).
*Manufacturing and Managing Customer-Driven Derivatives*. Wiley. ISBN 978-1-118-63262-8. - ↑ Espen Gaarder Haug,
*Derivatives Models on Models*, Wiley (July 24, 2007) 978-0470013229 - ↑ Richard R. Lindsey and Barry Schachter (editors),
*How I Became a Quant: Insights from 25 of Wall Street's Elite*, Wiley (August 3, 2009) 978-0470452578 - ↑ Emanuel Derman,
*My Life as a Quant: Reflections on Physics and Finance*, Wiley (September 16, 2004) 978-0471394204 - 1 2 Aaron Brown,
*Red-Blooded Risk: The Secret History of Wall Street*, Wiley (October 11, 2011) 978-1118043868 - ↑ Aaron Brown,
*The Poker Face of Wall Street*, Wiley (March 31, 2006) 978-0470127315 - ↑ Dan Stefanica,
*A Primer for the Mathematics of Financial Engineering*, FE Press (April 4, 2008) 978-0979757600 - ↑ "{title}". Archived from the original on 2013-04-10. Retrieved 2013-04-25.
- ↑ "The Department of Finance and Risk Engineering". Polytechnic Institute of NYU. Archived from the original on 2014-01-04. Retrieved 2012-05-09.
- ↑ Marek Capiski and Tomasz Zastawniak,
*Mathematics for Finance: An Introduction to Financial Engineering*, Springer (November 25, 2010) 978-0857290816 - ↑ David Ruppert,
*Statistics and Data Analysis for Financial Engineering*, Springer (November 17, 2010) 978-1441977861 - ↑ Nassim Nicholas Taleb,
*The Black Swan: The Impact of the Highly Improbable*, Random House (April 17, 2007) 978-1400063512 - ↑ "
*Whodunit? Rocket Scientists on Wall Street*". Minyanville. Archived from the original on 2012-07-11. Retrieved 2012-07-22. - ↑ "
*Recipe for Disaster: The Formula that Killed Wall Street*". Wired. February 23, 2009. Archived from the original on 2012-07-26. Retrieved 2012-07-22. - ↑ Stewart, Ian (February 12, 2012). "
*The Mathematical Equation that Caused the Banks to Crash*". London: Wired. Archived from the original on 2013-09-27. Retrieved 2012-07-22. - ↑ < Pablo Triana, The Number That Killed Us: A Story of Modern Banking, Flawed Mathematics, and a Big Financial Crisis
*, Wiley (December 6, 2011) 978-0470529737* - ↑ < Scott Patterson,
*The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It*, Crown Business (February 2, 2010) 978-0307453372 - ↑ < Scott Patterson,
*Dark Pools: High-Speed Traders, A.I. Bandits, and the Threat to the Global Financial System*, Crown Business (June 12, 2012) 978-0307887177 - ↑ Emanuel Derman,
*Models.Behaving.Badly.: Why Confusing Illusion with Reality Can Lead to Disaster, on Wall Street and in Life*, Free Press (July 24, 2012) 978-1439164990 - ↑ "Crisis may be worse than Depression, Volcker says". Reuters. Feb 20, 2009. Archived from the original on 2013-09-28. Retrieved 2013-09-05.

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