Entropic value at risk
In financial mathematics and stochastic optimization, the concept of risk measure is used to quantify the risk involved in a random outcome or risk position. Many risk measures have hitherto been prop
Risk measure
In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve. The purpose of this reserve is to make the risks t
Hyperbolic absolute risk aversion
In finance, economics, and decision theory, hyperbolic absolute risk aversion (HARA) refers to a type of risk aversion that is particularly convenient to model mathematically and to obtain empirical p
Deviation risk measure
In financial mathematics, a deviation risk measure is a function to quantify financial risk (and not necessarily downside risk) in a different method than a general risk measure. Deviation risk measur
Drawdown (economics)
The drawdown is the measure of the decline from a historical peak in some variable (typically the cumulative profit or total open equity of a financial trading strategy). Somewhat more formally, if is
Merton model
The Merton model, developed by Robert C. Merton in 1974, is a widely used credit risk model. Analysts and investors utilize the Merton model to understand how capable a company is at meeting financial
Discounted maximum loss
Discounted maximum loss, also known as worst-case risk measure, is the present value of the worst-case scenario for a financial portfolio. In investment, in order to protect the value of an investment
Solvency cone
The solvency cone is a concept used in financial mathematics which models the possible trades in the financial market. This is of particular interest to markets with transaction costs. Specifically, i
Time consistency (finance)
Time consistency in the context of finance is the property of not having mutually contradictory evaluations of risk at different points in time. This property implies that if investment A is considere
GovernmentRisk360
GovernmentRisk360 is a methodology designed to systematically capture the range of government related risk factors at play in an Australian domestic context. It was developed by and launched by FPL Ad
Modern portfolio theory
Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a
Risk aversion
In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to
Isoelastic utility
In economics, the isoelastic function for utility, also known as the isoelastic utility function, or power utility function, is used to express utility in terms of consumption or some other economic v
Capital asset pricing model
In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversi
Exponential utility
In economics and finance, exponential utility is a specific form of the utility function, used in some contexts because of its convenience when risk (sometimes referred to as uncertainty) is present,
Spectral risk measure
A Spectral risk measure is a risk measure given as a weighted average of outcomes where bad outcomes are, typically, included with larger weights. A spectral risk measure is a function of portfolio re
Superhedging price
The superhedging price is a coherent risk measure. The superhedging price of a portfolio (A) is equivalent to the smallest amount necessary to be paid for an admissible portfolio (B) at the current ti
Downside beta
In investing, downside beta is the beta that measures a stock's association with the overall stock market (risk) only on days when the market’s return is negative. Downside beta was first proposed by
Risk-neutral measure
In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price is exactly equal to the disco
Upside risk
In investing, upside risk is the uncertain possibility of gain. It is measured by upside beta. An alternative measure of upside risk is the upper semi-deviation. Upside risk is calculated using data o
Historical simulation (finance)
Historical simulation in finance's value at risk (VaR) analysis is a procedure for predicting the value at risk by 'simulating' or constructing the cumulative distribution function (CDF) of assets ret
Coherent risk measure
In the fields of actuarial science and financial economics there are a number of ways that risk can be defined; to clarify the concept theoreticians have described a number of properties that a risk m
Upside beta
In investing, upside beta is the element of traditional beta that investors do not typically associate with the true meaning of risk. It is defined to be the scaled amount by which an asset tends to m
Expected shortfall
Expected shortfall (ES) is a risk measure—a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is t
Acceptance set
In financial mathematics, acceptance set is a set of acceptable future net worth which is acceptable to the regulator. It is related to risk measures.
Distortion risk measure
In financial mathematics and economics, a distortion risk measure is a type of risk measure which is related to the cumulative distribution function of the return of a financial portfolio.
Dynamic risk measure
In financial mathematics, a conditional risk measure is a random variable of the financial risk (particularly the downside risk) as if measured at some point in the future. A risk measure can be thoug
Cascades in financial networks
Cascades in financial networks are situations in which the failure of one financial institution causes a cascading failure in another member of the financial network. In an extreme this can cause fail
Dual-beta
In investing, dual-beta is the idea that the single regular market beta can be usefully replaced with two finer-grained measures, a downside beta and an upside beta.
Betavexity
In investment analysis, betavexity is a form of convexity that is specific to the beta coefficient of a long tailed investment (i.e. mortality risk). It is similar in nature to bond convexity or gamma
Entropic risk measure
In financial mathematics (concerned with mathematical modeling of financial markets), the entropic risk measure is a risk measure which depends on the risk aversion of the user through the exponential
Extreme value theory
Extreme value theory or extreme value analysis (EVA) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It seeks to assess, from a given ordere
Value at risk
Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time pe
Financial risk modeling
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
Two-moment decision model
In decision theory, economics, and finance, a two-moment decision model is a model that describes or prescribes the process of making decisions in a context in which the decision-maker is faced with r
Omega ratio
The Omega ratio is a risk-return performance measure of an investment asset, portfolio, or strategy. It was devised by Con Keating and William F. Shadwick in 2002 and is defined as the probability wei
Downside risk
Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. Ris
Chan–Karolyi–Longstaff–Sanders process
In mathematics, the Chan–Karolyi–Longstaff–Sanders process (abbreviated as CKLS process) is a stochastic process with applications to finance. In particular it has been used to model the term structur
Multiple factor models
In mathematical finance, multiple factor models are asset pricing models that can be used to estimate the discount rate for the valuation of financial assets. They are generally extensions of the sing
XVA
An X-Value Adjustment (XVA, xVA) is an umbrella term referring to a number of different “valuation adjustments” that banks must make when assessing the value of derivative contracts that they have ent
RiskMetrics
The RiskMetrics variance model (also known as exponential smoother) was first established in 1989, when Sir Dennis Weatherstone, the new chairman of J.P. Morgan, asked for a daily report measuring and
Fama–French three-factor model
In asset pricing and portfolio management the Fama–French three-factor model is a statistical model designed in 1992 by Eugene Fama and Kenneth French to describe stock returns. Fama and French were c
Tail value at risk
Tail value at risk (TVaR), also known as tail conditional expectation (TCE) or conditional tail expectation (CTE), is a risk measure associated with the more general value at risk. It quantifies the e
Consistent pricing process
A consistent pricing process (CPP) is any representation of (frictionless) "prices" of assets in a market. It is a stochastic process in a filtered probability space such that at time the component ca
Jarrow–Turnbull model
The Jarrow–Turnbull model is a widely used "reduced-form" credit risk model. It was published in 1995 by Robert A. Jarrow and Stuart Turnbull. Under the model, which returns the corporate's probabilit
Diversification (finance)
In finance, diversification is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk. A common path towards diversification is to reduce risk or vola