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Benoit B.Mandelbrot was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.
Financial economics is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on both sides of a trade". Its concern is thus the interrelation of financial variables, such as share prices, interest rates and exchange rates, as opposed to those concerning the real economy. It has two main areas of focus: asset pricing and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital. It thus provides the theoretical underpinning for much of finance.
The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments, using various underlying assumptions. From the parabolic partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price given the risk of the security and its expected return. The equation and model are named after economists Fischer Black and Myron Scholes; Robert C. Merton, who first wrote an academic paper on the subject, is sometimes also credited.
Nassim Nicholas Taleb is a Lebanese-American essayist, mathematical statistician, former option trader, risk analyst, and aphorist whose work concerns problems of randomness, probability, and uncertainty.
A stock trader or equity trader or share trader, also called a stock investor, is a person or company involved in trading equity securities and attempting to profit from the purchase and sale of those securities. Stock traders may be an investor, agent, hedger, arbitrageur, speculator, or stockbroker. Such equity trading in large publicly traded companies may be through a stock exchange. Stock shares in smaller public companies may be bought and sold in over-the-counter (OTC) markets or in some instances in equity crowdfunding platforms.
A fat-tailed distribution is a probability distribution that exhibits a large skewness or kurtosis, relative to that of either a normal distribution or an exponential distribution. In common usage, the terms fat-tailed and heavy-tailed are sometimes synonymous; fat-tailed is sometimes also defined as a subset of heavy-tailed. Different research communities favor one or the other largely for historical reasons, and may have differences in the precise definition of either.
Financial risk modeling is the use of formal mathematical and econometric techniques to measure, monitor and control the market risk, credit risk, and operational risk on a firm's balance sheet, on a bank's trading book, or re a fund manager's portfolio value; see Financial risk management. Risk modeling is one of many subtasks within the broader area of financial modeling.
Skewness risk in financial modeling is the risk that results when observations are not spread symmetrically around an average value, but instead have a skewed distribution. As a result, the mean and the median can be different. Skewness risk can arise in any quantitative model that assumes a symmetric distribution but is applied to skewed data.
The black swan theory or theory of black swan events is a metaphor that describes an event that comes as a surprise, has a major effect, and is often inappropriately rationalized after the fact with the benefit of hindsight. The term is based on an ancient saying that presumed black swans did not exist – a saying that became reinterpreted to teach a different lesson after they were discovered in Australia.
Harold Edwin Hurst was a British hydrologist from Leicester. Hurst's (1951) study on measuring the long-term storage capacity of reservoirs documented the presence of long-range dependence in hydrology, especially concerning the fluctuations of the water level in the Nile River. In doing so, he developed the empirical rescaled range methodology for measuring long-range dependence. Much of Hurst's research was motivated by his empirical observations of the Nile. The Hurst exponent, which has been used in other fields, such as finance and cardiology, was named after him.
In finance, volatility is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns.
In economics and finance, a Taleb distribution is the statistical profile of an investment which normally provides a payoff of small positive returns, while carrying a small but significant risk of catastrophic losses. The term was coined by journalist Martin Wolf and economist John Kay to describe investments with a "high probability of a modest gain and a low probability of huge losses in any period."
Tail risk, sometimes called "fat tail risk," is the financial risk of an asset or portfolio of assets moving more than three standard deviations from its current price, above the risk of a normal distribution. Tail risks include low-probability events arising at both ends of a normal distribution curve, also known as tail events. However, as investors are generally more concerned with unexpected losses rather than gains, a debate about tail risk is focused on the left tail. Prudent asset managers are typically cautious with the tail involving losses which could damage or ruin portfolios, and not the beneficial tail of outsized gains.
The seven states of randomness in probability theory, fractals and risk analysis are extensions of the concept of randomness as modeled by the normal distribution. These seven states were first introduced by Benoît Mandelbrot in his 1997 book Fractals and Scaling in Finance, which applied fractal analysis to the study of risk and randomness. This classification builds upon the three main states of randomness: mild, slow, and wild.
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets.
The Lindy effect is a theorized phenomenon by which the future life expectancy of some non-perishable things, like a technology or an idea, is proportional to their current age. Thus, the Lindy effect proposes the longer a period something has survived to exist or be used in the present, the longer its remaining life expectancy. Longevity implies a resistance to change, obsolescence or competition and greater odds of continued existence into the future. Where the Lindy effect applies, mortality rate decreases with time. Mathematically, the Lindy effect corresponds to lifetimes following a Pareto probability distribution.
Edgar E. Peters, is an asset manager and writer on investment management topics. He is noted for his early contributions to the application of chaos theory and fractals to the financial markets. These works primarily dealt with fat tailed distributions originally discovered by Benoit Mandelbrot and expanded upon in Peters. These probability distributions are considered fractal because they are self-similar over different investment horizons once adjusted for scale.
In economics and finance, a holy grail distribution is a probability distribution with positive mean and right fat tail — a returns profile of a hypothetical investment vehicle that produces small returns centered on zero and occasionally exhibits outsized positive returns.
Stefan Mittnik is a German economist, currently holds the Chair of Financial Econometrics at the Ludwig Maximilian University of Munich. He is a fellow of the Center for Financial Studies and known for his work on financial market and financial risk modeling as well as macroeconometrics. He is also a co-founder of the German-British robo-advisor Scalable Capital.
References
- Mandelbrot, Benoit; Hudson, Richard L. (2004). The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward . New York: Basic Books. ISBN 0-465-04355-0.
- Premaratne, G., Bera, A. K. (2000). Modeling Asymmetry and Excess Kurtosis in Stock Return Data. Office of Research Working Paper Number 00-0123, University of Illinois