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Financial engineering is a multidisciplinary field involving financial theory, the methods of engineering, the tools of mathematics and the practice of programming. It has also been defined as the application of technical methods, especially from mathematical finance and computational finance, in the practice of finance. Despite its name, financial engineering does not belong to any of the fields in traditional engineering. In the United States, the Accreditation Board for Engineering and Technology (ABET) does not accredit financial engineering degrees. In the United States, financial engineering programs are accredited by the International Association of Financial Engineers.
Financial engineering draws on tools from applied mathematics, computer science, statistics and economic theory. In broadest definition, 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. 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. It is sometimes restricted even further, to cover only those originating new financial products and strategies.
Note: in January, 2014, the Polytechnic Institute of New York University changed its name to the New York University Polytechnic School of Engineering.
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. Mathematical finance is the application of theoretical mathematics to finance.
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. The difference is that is it 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.
“Rocket scientist” is an older term reserved for the first generation of financial quants who arrived on Wall Street in the late 1970s and early 1980s. While basically synonymous with financial engineer, it implies adventurousness and fondness for disruptive innovation. Rocket scientists were usually trained in applied mathematics, statistics or finance; and spent their entire careers in risk-taking. They were not hired for their mathematical talents, they either worked for themselves or applied mathematical techniques to traditional financial jobs. 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.
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.
An older use of the term "financial engineering" that is less common today is aggressive restructuring of corporate balance sheets. It is generally (but not always) a disparaging term, implying that someone is profiting from paper games at the expense of employees and investors.
The best known critic of financial engineering is Nassim Taleb, a professor of financial engineering at Polytechnic Institute of New York University  who argues that it replaces common sense and leads to disaster. Many other authors have identified specific problems in financial engineering that caused catastrophes: Aaron Brown named confusion between quants and regulators over the meaning of “capital”, Felix Salmon gently pointed to the Gaussian copula, Ian Stewart criticized the Black-Scholes formula, Pablo Triana dislikes value at risk and Scott Patterson  accused quantitative traders and later high-frequency traders.
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.