Quantitative finance

Computational finance (also known as financial engineering) is a cross-disciplinary field which relies on mathematical finance, numerical methods and computer simulations to make trading, hedging and investment decisions, as well as facilitating the risk management of those decisions. Utilizing various methods, practitioners of computational finance aim to precisely determine the financial risk that certain financial instruments create.

Areas where computational finance techniques are employed include:
 * Investment banking
 * Corporate strategic planning
 * Securities trading and financial risk management
 * Derivatives trading and risk management
 * Investment management

About
A quantitative analyst is a person who works in the financial markets developing mathematical models to assist the activities of traders and risk managers within banks and other large corporate institutions. Throughout the industry, such professionals are known as "quants"[1].

Historically quants often had a background in mathematics or physics, usually at a PhD level. Fischer Black, an originator of the Black Scholes model who might be viewed as the first quant, earned his PhD from Harvard in applied mathematics. However the rapid growth of the derivatives industry and increasing sophistication in the use of stochastic calculus to model the markets led to the creation of specialized Master's and PhD courses in mathematical finance, computational finance, and financial reinsurance. Following that, a large number of new quants have now recently completed those courses, often sponsored by private institutions.

Although the original quants were concerned with risk management and derivatives pricing, the meaning of the term has expanded over time to include those individuals involved in almost any application of mathematics in finance. An example is statistical arbitrage.

For an overview of the activities conducted by a quant see computational finance and derivative (finance).

Careers
Generally, individuals who fill positions in computational finance need quantitative skills in the mathematics of multivariate calculus, linear algebra, differential equations, probability theory, and statistical inference, and C++ has become the dominant computer language necessary due to the computationally intensive nature of many algorithms, and the focus on libraries rather than applications.

Computational finance was traditionally populated by Ph.D's in finance, physics and mathematics who moved into the field from more pure, academic backgrounds (either directly from graduate school, or after teaching or research) prior to the 1980’s. However, as the actual use of computers has become essential to rapidly carrying out computational finance decisions, a background in pure computer science is now also needed, and hence many computing graduates enter the field as well. Masters level degree holders are also increasingly making their presence felt as more terminal programs become available at the leading schools (whence field practitioners are almost exclusively recruited).

Today, all full service institutional finance firms employ computational finance professionals in their banking and finance operations (as opposed to being ancillary information technology specialists), while there are many other boutique firms ranging from 20 or fewer employees to several thousand that specialize in quantitative trading alone. JPMorgan Chase & Co. was one of the first firms to create a large derivatives business and employ computational finance in the real world, while D.E. Shaw is probably the oldest and largest quant fund (Citadel Investments is a major rival).

Universities
Some of the top universities that offer a program in quantitative finance, mathematical engineering/finance or similar, are:
 * Carnegie Mellon University (Master in Computational Finance)
 * Princeton University (Master In Finance)
 * Columbia University (Financial Engineering)
 * New York University (Mathematics in Finance)
 * Erasmus University (Master in Quantitative Finance, Bachelor in Financial Econometrics)
 * Stanford University (Financial Mathematics)
 * University of California, Berkeley (Financial Engineering)
 * University of California, Los Angeles (Financial Engineering)
 * University of Chicago (Financial Mathematics)
 * Cornell University (MEng, FE concentration)
 * London School of Economics (Financial Mathematics)