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. 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.
Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose, given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses.
Market risk is the risk of losses in positions arising from movements in market variables like prices and volatility. There is no unique classification as each classification may refer to different aspects of market risk. Nevertheless, the most commonly used types of market risk are:
In finance, the Sharpe ratio measures the performance of an investment such as a security or portfolio compared to a risk-free asset, after adjusting for its risk. It is defined as the difference between the returns of the investment and the risk-free return, divided by the standard deviation of the investment returns. It represents the additional amount of return that an investor receives per unit of increase in risk.
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. The Sunday Times called his 2007 book The Black Swan one of the 12 most influential books since World War II.
In finance, statistical arbitrage is a class of short-term financial trading strategies that employ mean reversion models involving broadly diversified portfolios of securities held for short periods of time. These strategies are supported by substantial mathematical, computational, and trading platforms.
Risk arbitrage, also known as merger arbitrage, is an investment strategy that speculates on the successful completion of mergers and acquisitions. An investor that employs this strategy is known as an arbitrageur. Risk arbitrage is a type of event-driven investing in that it attempts to exploit pricing inefficiencies caused by a corporate event.
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.
In statistics and decision theory, kurtosis risk is the risk that results when a statistical model assumes the normal distribution, but is applied to observations that have a tendency to occasionally be much farther from the average than is expected for a normal distribution.
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.
Post-Modern Portfolio Theory (PMPT) is an extension of the traditional Modern Portfolio Theory (MPT), an application of mean-variance analysis (MVA). Both theories propose how rational investors can use diversification to optimize their portfolios.
In finance, model risk is the risk of loss resulting from using insufficiently accurate models to make decisions, originally and frequently in the context of valuing financial securities. However, model risk is more and more prevalent in activities other than financial securities valuation, such as assigning consumer credit scores, real-time probability prediction of fraudulent credit card transactions, and computing the probability of air flight passenger being a terrorist. Rebonato in 2002 defines model risk as "the risk of occurrence of a significant difference between the mark-to-model value of a complex and/or illiquid instrument, and the price at which the same instrument is revealed to have traded in the market".
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.
Empirica Capital LLC was a hedge fund founded in 1999 by Nassim Nicholas Taleb in partnership with Mark Spitznagel, that used Taleb's black swan strategy. The firm closed in 2005 as Taleb took time off for health reasons.
Convergence trade is a trading strategy consisting of two positions: buying one asset forward—i.e., for delivery in future —and selling a similar asset forward for a higher price, in the expectation that by the time the assets must be delivered, the prices will have become closer to equal, and thus one profits by the amount of convergence.
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.
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.
