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Copula (probability theory)

Index Copula (probability theory)

In probability theory and statistics, a copula is a multivariate probability distribution for which the marginal probability distribution of each variable is uniform. [1]

72 relations: Abe Sklar, Absolute continuity, Actuary, Agent-based computational economics, Annals of Statistics, Basket option, Bernstein's theorem on monotone functions, Cartesian product, Collateralized debt obligation, Comonotonicity, Constant maturity swap, Convex function, Copula (linguistics), Correlation and dependence, Credit derivative, Cumulative distribution function, David Clayton, Dependent and independent variables, Derivative (finance), Emergence, Emil Julius Gumbel, Equity derivative, Exotic derivative, Extreme value theory, Financial crisis, Financial crisis of 2007–2008, Financial risk modeling, Financial Times, Flight-to-quality, Foreign exchange derivative, Herd behavior, Hyperrectangle, Implied volatility, Independence (probability theory), Interest rate derivative, Investment management, Joint probability distribution, Journal of Futures Markets, Linguistics, Marginal distribution, Mathematical finance, Maurice René Fréchet, Mir Maswood Ali, Monte Carlo methods in finance, Multivariable calculus, Multivariate normal distribution, Pairs trade, Portfolio optimization, Probability integral transform, Probability theory, ..., Pseudorandomness, Random variable, Range (mathematics), Reliability (statistics), Risk management, Securitization, Simulation, Spread option, Statistical arbitrage, Statistics, Stress test (financial), Systemic risk, Tail risk, Two-moment decision model, Uniform distribution (continuous), Unit cube, University of Edinburgh School of Social and Political Sciences, Value at risk, Vine copula, Volatility smile, Warranty, Wassily Hoeffding. Expand index (22 more) »

Abe Sklar

Abe Sklar is an American mathematician, a professor emeritus of applied mathematics at the Illinois Institute of Technology.

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Absolute continuity

In calculus, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity.

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An actuary is a business professional who deals with the measurement and management of risk and uncertainty.

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Agent-based computational economics

Agent-based computational economics (ACE) is the area of computational economics that studies economic processes, including whole economies, as dynamic systems of interacting agents.

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Annals of Statistics

The Annals of Statistics is a peer-reviewed statistics journal published by the Institute of Mathematical Statistics.

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Basket option

A basket option is a financial derivative, more specifically an exotic option, whose underlying is a weighted sum or average of different assets that have been grouped together in a basket.

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Bernstein's theorem on monotone functions

In real analysis, a branch of mathematics, Bernstein's theorem states that every real-valued function on the half-line.

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Cartesian product

In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.

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Collateralized debt obligation

A collateralized debt obligation (CDO) is a type of structured asset-backed security (ABS).

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In probability theory, comonotonicity mainly refers to the perfect positive dependence between the components of a random vector, essentially saying that they can be represented as increasing functions of a single random variable.

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Constant maturity swap

A constant maturity swap, also known as a CMS, is a swap that allows the purchaser to fix the duration of received flows on a swap.

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Convex function

In mathematics, a real-valued function defined on an ''n''-dimensional interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions.

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Copula (linguistics)

In linguistics, a copula (plural: copulas or copulae; abbreviated) is a word used to link the subject of a sentence with a predicate (a subject complement), such as the word is in the sentence "The sky is blue." The word copula derives from the Latin noun for a "link" or "tie" that connects two different things.

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Correlation and dependence

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data.

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Credit derivative

In finance, a credit derivative refers to any one of "various instruments and techniques designed to separate and then transfer the credit risk"The Economist Passing on the risks 2 November 1996 or the risk of an event of default of a corporate or sovereign borrower, transferring it to an entity other than the lender or debtholder.

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Cumulative distribution function

In probability theory and statistics, the cumulative distribution function (CDF, also cumulative density function) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.

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David Clayton

David George Clayton, born 13 June 1944, is a British statistician and epidemiologist.

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Dependent and independent variables

In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.

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Derivative (finance)

In finance, a derivative is a contract that derives its value from the performance of an underlying entity.

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In philosophy, systems theory, science, and art, emergence occurs when "the whole is greater than the sum of the parts," meaning the whole has properties its parts do not have.

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Emil Julius Gumbel

Emil Julius Gumbel (18 July 1891, Munich – 10 September 1966, New York City) was a German mathematician and political writer.

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Equity derivative

In finance, an equity derivative is a class of derivatives whose value is at least partly derived from one or more underlying equity securities.

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Exotic derivative

An exotic derivative, in finance, is a derivative which is more complex than commonly traded "vanilla" products.

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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.

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Financial crisis

A financial crisis is any of a broad variety of situations in which some financial assets suddenly lose a large part of their nominal value.

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Financial crisis of 2007–2008

The financial crisis of 2007–2008, also known as the global financial crisis and the 2008 financial crisis, is considered by many economists to have been the worst financial crisis since the Great Depression of the 1930s.

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Financial risk modeling

Financial risk modeling refers to the use of formal econometric techniques to determine the aggregate risk in a financial portfolio.

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Financial Times

The Financial Times (FT) is a Japanese-owned (since 2015), English-language international daily newspaper headquartered in London, with a special emphasis on business and economic news.

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A flight-to-quality, or flight-to-safety, is a financial market phenomenon occurring when investors sell what they perceive to be higher-risk investments and purchase safer investments, such as US Treasuries or gold.

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Foreign exchange derivative

A foreign exchange derivative is a financial derivative whose payoff depends on the foreign exchange rate(s) of two (or more) currencies.

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Herd behavior

Herd behavior describes how individuals in a group can act collectively without centralized direction.

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In geometry, an n-orthotopeCoxeter, 1973 (also called a hyperrectangle or a box) is the generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of intervals.

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Implied volatility

In financial mathematics, the implied volatility of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes) will return a theoretical value equal to the current market price of the option.

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Independence (probability theory)

In probability theory, two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.

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Interest rate derivative

In finance, an interest rate derivative (IRD) is a derivative whose payments are determined through calculation techniques where the underlying benchmark product is an interest rate, or set of different interest rates.

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Investment management

Investment management is the professional asset management of various securities (shares, bonds and other securities) and other assets (e.g., real estate) in order to meet specified investment goals for the benefit of the investors.

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Joint probability distribution

Given random variables X, Y,..., that are defined on a probability space, the joint probability distribution for X, Y,...

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Journal of Futures Markets

Journal of Futures Markets is a monthly peer-reviewed academic journal covers developments in financial futures and derivatives.

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Linguistics is the scientific study of language, and involves an analysis of language form, language meaning, and language in context.

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Marginal distribution

In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset.

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Mathematical finance

Mathematical finance, also known as quantitative finance, is a field of applied mathematics, concerned with mathematical modeling of financial markets.

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Maurice René Fréchet

Maurice Fréchet (2 September 1878 – 4 June 1973) was a French mathematician.

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Mir Maswood Ali

Mir Maswood Ali (12 March 1929 – 18 August 2009) was a Canadian statistician and mathematician of Bengali origin.

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Monte Carlo methods in finance

Monte Carlo methods are used in finance and mathematical finance to value and analyze (complex) instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining the distribution of their value over the range of resultant outcomes.

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Multivariable calculus

Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables, rather than just one.

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Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions.

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Pairs trade

The pairs trade or pair trading is a market neutral trading strategy enabling traders to profit from virtually any market conditions: uptrend, downtrend, or sideways movement.

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Portfolio optimization

Portfolio optimization is the process of selecting the best portfolio (asset distribution), out of the set of all portfolios being considered, according to some objective.

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Probability integral transform

In statistics, the probability integral transform or transformation relates to the result that data values that are modelled as being random variables from any given continuous distribution can be converted to random variables having a standard uniform distribution.

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Probability theory

Probability theory is the branch of mathematics concerned with probability.

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A pseudorandom process is a process that appears to be random but is not.

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Random variable

In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.

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Range (mathematics)

In mathematics, and more specifically in naive set theory, the range of a function refers to either the codomain or the image of the function, depending upon usage.

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Reliability (statistics)

Reliability in statistics and psychometrics is the overall consistency of a measure.

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Risk management

Risk management is the identification, evaluation, and prioritization of risks (defined in ISO 31000 as the effect of uncertainty on objectives) followed by coordinator and economical application of resources to minimize, monitor, and control the probability or impact of unfortunate events or to maximize the realization of opportunities.

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Securitization is the financial practice of pooling various types of contractual debt such as residential mortgages, commercial mortgages, auto loans or credit card debt obligations (or other non-debt assets which generate receivables) and selling their related cash flows to third party investors as securities, which may be described as bonds, pass-through securities, or collateralized debt obligations (CDOs).

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Simulation is the imitation of the operation of a real-world process or system.

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Spread option

In finance, a spread option is a type of option where the payoff is based on the difference in price between two underlying assets.

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Statistical arbitrage

In finance, statistical arbitrage (often abbreviated as Stat Arb or StatArb) is a class of short-term financial trading strategies that employ mean reversion models involving broadly diversified portfolios of securities (hundreds to thousands) held for short periods of time (generally seconds to days).

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Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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Stress test (financial)

A stress test, in financial terminology, is an analysis or simulation designed to determine the ability of a given financial instrument or financial institution to deal with an economic crisis.

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Systemic risk

In finance, systemic risk is the risk of collapse of an entire financial system or entire market, as opposed to risk associated with any one individual entity, group or component of a system, that can be contained therein without harming the entire system.

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Tail risk

Tail risk is the additional risk of an asset or portfolio of assets moving more than 3 standard deviations from its current price, above the risk of a normal distribution.

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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 random variables whose realizations cannot be known in advance, and in which choices are made based on knowledge of two moments of those random variables.

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Uniform distribution (continuous)

In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.

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Unit cube

A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long.

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University of Edinburgh School of Social and Political Sciences

The School of Social and Political Sciences at the University of Edinburgh is a department undertaking research and teaching into politics, international relations, social anthropology, social policy, social work and sociology.

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Value at risk

Value at risk (VaR) is a measure of the risk of loss for investments.

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Vine copula

A vine is a graphical tool for labeling constraints in high-dimensional probability distributions.

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Volatility smile

Volatility smiles are implied volatility patterns that arise in pricing financial options.

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In contract law, a warranty has various meanings but generally means a guarantee or promise which provides assurance by one party to the other party that specific facts or conditions are true or will happen.

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Wassily Hoeffding

Wassily Hoeffding (June 12, 1914 – February 28, 1991) was a Finnish statistician and probabilist.

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Archimedean copula, Copula (mathematics), Copula (statistics), Copula Methods, Copula function, Frechet-Hoeffding copula bounds, Fréchet-Hoeffding copula bounds, Fréchet–Hoeffding copula bounds, Gaussian copula, Gaussian copula function, Gaussian copula model, N-increasing, N-increasing function, Sklar theorem, Sklar's theorem, Sklars theorem, Stochastic copula.


[1] https://en.wikipedia.org/wiki/Copula_(probability_theory)

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