Quantitative analysis (finance)

Source: Wikipedia, the free encyclopedia.

Quantitative analysis is the use of

industrial mathematics in other industries.[1] The process usually consists of searching vast databases for patterns, such as correlations among liquid assets or price-movement patterns (trend following or reversion
).

Although the original quantitative analysts were "sell side quants" from market maker firms, 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 mathematical finance, including the buy side.[2] Applied quantitative analysis is commonly associated with quantitative investment management which includes a variety of methods such as statistical arbitrage, algorithmic trading and electronic trading.

Some of the larger investment managers using quantitative analysis include

AQR Capital Management.[3]

History

Further information: Mathematical finance § Derivatives pricing: the Q world, Financial economics § Derivative pricing, and § Seminal publications

Quantitative finance started in 1900 with Louis Bachelier's doctoral thesis "Theory of Speculation", which provided a model to price options under a normal distribution. Harry Markowitz's 1952 doctoral thesis "Portfolio Selection" and its published version was one of the first efforts in economics journals to formally adapt mathematical concepts to finance (mathematics was until then confined to specialized economics journals).[4] 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 Itô calculus
, management of risk in a quantifiable manner underlies much of the modern theory.

Modern

quantitative investment management was first introduced from the research of Edward Thorp, a mathematics professor at New Mexico State University (1961–1965) and University of California, Irvine (1965–1977).[5] Considered the "Father of Quantitative Investing",[5] Thorp sought to predict and simulate blackjack, a card-game he played in Las Vegas casinos.[6] He was able to create a system, known broadly as card counting, which used probability theory and statistical analysis to successfully win blackjack games.[6] His research was subsequently used during the 1980s and 1990s by investment management firms seeking to generate systematic and consistent returns in the U.S. stock market.[6]
The field has grown to incorporate numerous approaches and techniques; see Outline of finance § Quantitative investing, Post-modern portfolio theory, Financial economics § Portfolio theory.

In 1965

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.

contingent claim analysis
. Emanuel Derman's 2004 book My Life as a Quant helped to both make the role of a quantitative analyst better known outside of finance, and to popularize the abbreviation "quant" for a quantitative analyst.[10]

After the

risk neutral world", entailing three major developments; see Valuation of options § Post crisis
: (i) Option pricing and hedging inhere the relevant
volatility surface - to some extent, equity-option prices have incorporated the volatility smile since the 1987 crash - and banks then apply "surface aware" local- or stochastic volatility
models; (ii) The risk neutral value is adjusted for the impact of counter-party credit risk via a credit valuation adjustment, or CVA, as well as various of the other XVA; (iii) For discounting, the
multi-curve framework
" (
TONAR
, necessitating technical changes to the latter framework, while the underlying logic is unaffected).

Education

See also: Outline of finance § Education, Financial engineering § Education, Financial modeling § Quantitative finance, and Financial analyst § Qualification

Quantitative analysts often come from

PhD degrees
.

Typically, a quantitative analyst will also need extensive skills in computer programming, most commonly

Mathematica, and Python
. Data science and machine learning analysis and modelling methods are being increasingly employed in portfolio performance and portfolio risk modelling,[11][12] and as such data science and machine learning Master's graduates are also hired as quantitative analysts.

This demand for quantitative analysts has led to the creation of specialized Masters and PhD courses in financial engineering, mathematical finance,

machine learning, and financial analysis are becoming more popular with students and with employers. See Master of Quantitative Finance
for general discussion.

This has in parallel led to a resurgence in demand for

CQF
. The more general Master of Finance (and Master of Financial Economics) increasingly includes a significant technical component.

Types

Front office quantitative analyst

In

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.

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.

Increasingly, quants are attached to specific desks. Two cases are:

counterparty risk as well as (minimizing) the capital requirements under Basel III; and structurers, tasked with the design and manufacture
of client specific solutions.

Quantitative investment management

Further information: Quantitative fund
See also: Outline of finance § Quantitative investing

Quantitative analysis is used extensively by

asset managers. Some, such as FQ, 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
.

One of the first quantitative investment funds to launch was based in Santa Fe, New Mexico and began trading in 1991 under the name Prediction Company.[6][13] By the late-1990s, Prediction Company began using statistical arbitrage to secure investment returns, along with three other funds at the time, Renaissance Technologies and D. E. Shaw & Co, both based in New York.[6] Prediction hired scientists and computer programmers from the neighboring Los Alamos National Laboratory to create sophisticated statistical models using "industrial-strength computers" in order to "[build] the Supercollider of Finance".[14][15]

Machine learning models are now capable of identifying complex patterns in financial market data. With the aid of artificial intelligence, investors are increasingly turning to deep learning techniques to forecast and analyze trends in stock and foreign exchange markets.[16] See Applications of artificial intelligence § Trading and investment.

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

finite difference methods
, as well as the nature of the products being modeled.

Algorithmic trading quantitative analyst

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.

Risk management

Further information: Financial risk management § Banking, Investment banking § Risk management, and Bank § Capital and risk

This area has grown in importance in recent years, as the credit crisis exposed holes in the mechanisms used to ensure that positions were correctly

FRTB, Tail risk § Role of the global financial crisis (2007-2008)
. A core technique continues to be value at risk - applying both
Conditional value at risk and Extreme value theory
- while this is supplemented with various forms of
desk level
, and, as below, assessment of the models used by the bank's various divisions.

Innovation

In the aftermath of the financial crisis[2008], 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.

Model validation

Model validation (MV) takes the models and methods developed by front office, library, and modeling quantitative analysts and determines their validity and correctness; see model risk. The MV group might well be seen as a superset of the quantitative operations in a financial institution, since it must deal with new and advanced models and trading techniques from across the firm.

Post crisis, regulators now typically talk directly to the quants in the middle office - such as the model validators - and since profits highly depend on the regulatory infrastructure, model validation has gained in weight and importance with respect to the quants in the front office.

Before the crisis however, the pay structure in all firms was such that MV groups struggle to attract and retain adequate staff, often with talented quantitative analysts leaving at the first opportunity. This gravely impacted corporate ability to manage model risk, or to ensure that the positions being held were correctly valued. An MV quantitative analyst would typically earn a fraction of quantitative analysts in other groups with similar length of experience. In the years following the crisis, as mentioned, this has changed.

Quantitative developer

Quantitative developers, sometimes called quantitative software engineers, or quantitative engineers, are computer specialists that assist, implement and maintain the quantitative models. They tend to be highly specialised language technicians that bridge the gap between

software engineers and quantitative analysts. The term is also sometimes used outside the finance industry to refer to those working at the intersection of software engineering and quantitative research
.

Mathematical and statistical approaches

Further information: Mathematical finance, Financial modeling § Quantitative finance, Outline of finance § Mathematical tools, and Financial economics § Derivative pricing

Because of their backgrounds, quantitative analysts draw from various forms of mathematics: statistics and probability, calculus centered around partial differential equations, linear algebra, discrete mathematics, and econometrics. Some on the buy side may use machine learning. The majority of quantitative analysts have received little formal education in mainstream economics, and often apply a mindset drawn from the physical sciences. Quants use mathematical skills learned from diverse fields such as computer science, physics and engineering. These skills include (but are not limited to) advanced statistics, linear algebra and partial differential equations as well as solutions to these based upon numerical analysis.

Commonly used numerical methods are:

Techniques

A typical problem for a mathematically oriented quantitative analyst would be to develop a model for pricing, hedging, and risk-managing a complex derivative product. These quantitative analysts tend to rely more on numerical analysis than statistics and econometrics. One of the principal mathematical tools of quantitative finance is stochastic calculus. The mindset, however, is to prefer 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.

Academic and technical field journals

Areas of work

Seminal publications

See also

References

  1. ^ See Definition in the Society for Applied and Industrial Mathematics https://web.archive.org/web/20060430115935/http://siam.org/about/pdf/brochure.pdf
  2. ^ Derman, E. (2004). My life as a quant: reflections on physics and finance. John Wiley & Sons.
  3. ^ "Top Quantitative Hedge Funds". Street of Walls.
  4. S2CID 7492997
    .
  5. ^ a b Lam, Leslie P. Norton and Dan. "Why Edward Thorp Owns Only Berkshire Hathaway". barrons.com. Retrieved 2021-06-06.
  6. ^
    ISBN 978-0-307-45339-6
    .
  7. ^ Samuelson, P. A. (1965). "Rational Theory of Warrant Pricing". Industrial Management Review. 6 (2): 13–32.
  8. ^ Henry McKean the co-founder of stochastic calculus (along with Kiyosi Itô) wrote the appendix: see McKean, H. P. Jr. (1965). "Appendix (to Samuelson): a free boundary problem for the heat equation arising from a problem of mathematical economics". Industrial Management Review. 6 (2): 32–39.
  9. doi:10.1016/0304-4149(81)90026-0
    .
  10. ^ Derman, Emanuel (2004). My Life as a Quant. John Wiley and Sons.
  11. ^ "Machine Learning in Finance: Theory and Applications". marketsmedia.com. 22 January 2013. Retrieved 2 April 2018.
  12. ^ "A Machine-Learning View of Quantitative Finance" (PDF). qminitiative.org.
  13. ^ Rothschild, John (November 7, 1999). "The Gnomes of Santa Fe". archive.nytimes.com. Archived from the original on Jun 6, 2021. Retrieved May 6, 2021.
  14. ISSN 1059-1028
    . Retrieved May 6, 2021.
  15. ^ Beilselki, Vincent (September 6, 2018). "Millennium Shuts Down Pioneering Quant Hedge Fund". Bloomberg.com. Retrieved May 6, 2021.
  16. ISSN 2076-3417
    .
  17. ^ "The Journal of Portfolio Management". jpm.iijournals.com. Retrieved 2019-02-02.
  18. ^ "Quantitative Finance". Taylor & Francis.
  19. ^ "Finance and Stochastics – incl. Option to publish open access".

Further reading

External links

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