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# Quantitative analysis (finance)

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### Quantitative analysis (finance)

A quantitative analyst or quant is a person who specializes in the application of mathematical and statistical methods – such as numerical or quantitative techniques – to financial and risk management problems. Similar work of industrial mathematics is done in most other modern industries, but the work is not always called quantitative analysis.[1] See List of quantitative analysts.

Although the original quantitative analysts were "sell side quants" concerned with derivatives pricing and risk management, the meaning of the term has expanded over time to include those individuals involved in almost any application of mathematics in finance, including the "buy side".[2] Examples include statistical arbitrage, quantitative investment management, algorithmic trading, and electronic market making.

## History

Robert C. Merton, one of the pioneers of quantitative analysis, promoted stochastic calculus into the study of finance.

Quantitative finance started in 1900 with Louis Bachelier's doctoral thesis Theory of Speculation.

Harry Markowitz's 1952 Ph.D thesis "Portfolio Selection" and its published version [3] was one of the first efforts in economic journals to formally adapt mathematical concepts to finance. Markowitz formalized a notion of mean return and covariances for common stocks which allowed him to quantify the concept of "diversification" in a market. He showed how to compute the mean return and variance for a given portfolio and argued that investors should hold only those portfolios whose variance is minimal among all portfolios with a given mean return. Although the language of finance now involves Itō calculus, management of risk in a quantifiable manner underlies much of the modern theory.

In 1965 Paul Samuelson introduced stochastic calculus into the study of finance.[4][5] In 1969 Robert Merton promoted continuous stochastic calculus and continuous time processes. Merton was motivated by the desire to understand how prices are set in financial markets, which is the classical economics question of "equilibrium," and in later papers he used the machinery of stochastic calculus to begin investigation of this issue.

At the same time as Merton's work and with Merton's assistance, Fischer Black and Myron Scholes developed the Black–Scholes model, which was awarded the 1997 Nobel Memorial Prize in Economic Sciences. It provided a solution for a practical problem, that of finding a fair price for a European call option, i.e., the right to buy one share of a given stock at a specified price and time. Such options are frequently purchased by investors as a risk-hedging device. In 1981, Harrison and Pliska used the general theory of continuous-time stochastic processes to put the Black–Scholes model on a solid theoretical basis, and showed how to price numerous other derivative securities.[6]

## Education

Quantitative analysts often come from mathematics, physics or engineering backgrounds rather than economics-related fields, and quantitative analysis is a major source of employment for people with mathematics and physics Ph.D. degrees in the US education system, or with financial mathematics D.E.A. degrees (Univ. Paris VI, Univ. Paris VII, ParisTech...) in the French education system. Typically, a quantitative analyst will also need extensive skills in computer programming, most commonly C, C++, Java, and MATLAB.

This demand for quantitative analysts has led to a resurgence in demand for actuarial qualifications as well as creation of specialized Masters and PhD courses in financial engineering, mathematical finance, computational finance, and/or financial reinsurance. In particular, Masters degrees in mathematical finance, financial engineering, Operations Research and financial analysis are becoming more popular with students and with employers. See Master of Quantitative Finance; Master of Financial Economics.

## Types of quantitative analysts

### Front office quantitative analyst

In trading and sales operations, quantitative analysts work to determine prices, manage risk, and identify profitable opportunities. Historically this was a distinct activity from trading but the boundary between a desk quantitative analyst and a quantitative trader is increasingly blurred, and it is now difficult to enter trading as a profession without at least some quantitative analysis education. In the field of algorithmic trading it has reached the point where there is little meaningful difference. Front office work favours a higher speed to quality ratio, with a greater emphasis on solutions to specific problems than detailed modeling. FOQs typically are significantly better paid than those in back office, risk, and model validation. Although highly skilled analysts, FOQs frequently lack software engineering experience or formal training, and bound by time constraints and business pressures tactical solutions are often adopted.

### Quantitative investment management

Quantitative analysis is used extensively by asset managers. Some, such as AQR or Barclays, rely almost exclusively on quantitative strategies while others, such as Pimco, Blackrock or Citadel use a mix of quantitative and fundamental methods. Virtually all large asset managers and hedge funds rely to some degree on quantitative methods.[7]

### Library quantitative analysis

Major firms invest large sums in an attempt to produce standard methods of evaluating prices and risk. These differ from front office tools in that Excel is very rare, with most development being in C++, though Java and C# are sometimes used in non-performance critical tasks. LQs spend more time modeling ensuring the analytics are both efficient and correct, though there is tension between LQs and FOQs on the validity of their results. LQs are required to understand techniques such as Monte Carlo methods and finite difference methods, as well as the nature of the products being modeled.

Often the highest paid form of Quant, ATQs make use of methods taken from signal processing, game theory, gambling Kelly criterion, market microstructure, econometrics, and time series analysis. Algorithmic trading includes statistical arbitrage, but includes techniques largely based upon speed of response, to the extent that some ATQs modify hardware and Linux kernels to achieve ultra low latency.

### Risk management

This has grown in importance in recent years, as the credit crisis exposed holes in the mechanisms used to ensure that positions were correctly hedged, though in no bank does the pay in risk approach that in front office. A core technique is value at risk, and this is backed up with various forms of stress test (financial), economic capital analysis and direct analysis of the positions and models used by various bank's divisions.

### Innovation

In the aftermath of the financial crisis, there surfaced the recognition that quantitative valuation methods were generally too narrow in their approach. An agreed upon fix adopted by numerous financial institutions has been to improve collaboration through continuous improvement and thoughtful leadership. This has led to the creation of collaborative environments in order to produce the most robust statistical models available. Through working with a large pool of some of the world's most talented quantitative analysts, economists and mathematicians from the financial industry and academia, transparency continues to be improved, leading to constant improvement.

### Model validation

Model validation (MV) takes the models and methods developed by front office, library, and modeling quants and determines their validity and correctness. The MV group might well be seen as a superset of the quant operations in a financial institution, since it must deal with new and advanced models and trading techniques from across the firm. However, the pay structure in all firms is such that MV groups struggle to attract and retain adequate staff, often with talented quantitative analysts leaving at the first opportunity. This gravely impacts corporate ability to manage model risk, or to ensure that the positions being held are correctly valued. A MV quantitative analyst will typically earn a fraction of quantitative analysts in other groups with similar length of experience.

### Quantitative developer

Quant developers are computer specialists that assist, implement and maintain the quant models. They tend to be highly specialised language technicians that bridge the gap between software developer and quantitative analysts.

## Mathematical and statistical approaches

Because of their backgrounds, quantitative analysts draw from three forms of mathematics: statistics and probability, calculus centered around partial differential equations, and econometrics. The majority of quantitative analysts have received little formal education in mainstream economics, and often apply a mindset drawn from the physical sciences. Physicists tend to have significantly less experience of statistical techniques, and thus lean on approaches based upon partial differential equations, and solutions to these based upon numerical analysis.

The most commonly used numerical methods are:

## Techniques

A typical problem for a numerically oriented quantitative analyst would be to develop a model for pricing, hedging, and risk-managing a complex derivative product. Mathematically oriented quantitative analysts tend to have more of a reliance on numerical analysis, and less of a reliance on statistics and econometrics. These quantitative analysts tend to be of the psychology that prefers a deterministically "correct" answer, as once there is agreement on input values and market variable dynamics, there is only one correct price for any given security (which can be demonstrated, albeit often inefficiently, through a large volume of Monte Carlo simulations).

A typical problem for a statistically oriented quantitative analyst would be to develop a model for deciding which stocks are relatively expensive and which stocks are relatively cheap. The model might include a company's book value to price ratio, its trailing earnings to price ratio, and other accounting factors. An investment manager might implement this analysis by buying the underpriced stocks, selling the overpriced stocks, or both. Statistically oriented quantitative analysts tend to have more of a reliance on statistics and econometrics, and less of a reliance on sophisticated numerical techniques and object-oriented programming. These quantitative analysts tend to be of the psychology that enjoys trying to find the best approach to modeling data, and can accept that there is no "right answer" until time has passed and we can retrospectively see how the model performed. Both types of quantitative analysts demand a strong knowledge of sophisticated mathematics and computer programming proficiency.

One of the principal mathematical tools of quantitative finance is stochastic calculus.

## Areas of work

• Portfolio optimization
• Derivatives pricing and hedging: involves a lot of highly efficient (usually object-oriented) software development, advanced numerical techniques, and stochastic calculus
• Risk management: involves a lot of time series analysis, calibration, and backtesting for an example of Back Testing see Quantech Investments*Credit analysis

## References

1. ^ See Definition in the Society for Applied and Industrial Mathematics http://www.siam.org/about/pdf/brochure.pdf
2. ^ Derman, E. (2004). My life as a quant: reflections on physics and finance. John Wiley & Sons.
3. ^ Markowitz, H. (1952). Portfolio selection*. The journal of finance, 7(1), 77-91.
4. ^ Samuelson, P.A. (1965), ‘‘Rational theory of warrant pricing’’, Industrial Management Review, Vol. 6 No. 2, pp. 13-32
5. ^ Henry McKean the co-founder of stochastic calculus (along with K Ito) wrote the appendix: see McKean, H.P. Jr (1965), ‘‘Appendix (to Samueson): a free boundary problem for the heat equation arising from a problem of mathematical economics’’, Industrial Management Review, Vol. 6 No. 2, pp. 32-9.
6. ^ Harrison, J. Michael and Pliska, Stanley R., "Martingales and Stochastic Integrals in the Theory of Continuous Trading", in Stochastic Processes and their Applications, North Holland Publishing Company, 1981. Harrison and Pliska paper
7. ^ Quantitative Methods