An Introduction to Copulas

By Bill Ravens. 2000

6,428 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

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Citations in the corpus

The Variational Gaussian Process (2015, methodology): “Using techniques common in copula literature (Nelsen, 2006), the optimal function is Imagine generating samples z using this function.”
Hierarchical Variational Models (2015, methodology): “For example, copulas explicitly introduce dependence among d random variables by using joint distributions on d -dimensional hypercubes (Nelsen, 2006).”
Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications (2006, positive): “The copula concept dates back to seminal papers by Hoeffding and Sklar; recent methodological overviews are given for example by Joe (1997) and Nelsen (1999).”
Multi-period hedge ratios for a multi-asset portfolio when accounting for returns comovement (2008, background): “The existence of the function C is established by Sklar’s theorem (see Nelsen, 1999, section 2.10).”
On the power of generalized extreme value (GEV) and generalized Pareto distribution (GPD) estimators for empirical distributions of stock returns (2006, background): “Recall that a copula is the mathematical embodiment of the dependence structure between different random variables (Joe, 1997; Nelsen, 1998).”
Copula-Based Models for Financial Time Series (2009, methodology): “The Clayton and Gumbel copulas are discussed in Nelsen (2006), equations 4.2.1 and 4.2.4 respectively.”
Portfolio Value‐at‐Risk with Heavy‐Tailed Risk Factors (2002, neutral): “(For background on copulas see Nelsen 1999; for applications in risk management see Embrechts et al. 2002 and Li 2000.)”
Hierarchies of Archimedean copulas (2010, neutral): “For a general introduction to copulas we refer the reader to Nelsen (2006).”
Reliability Modeling for Systems with Multiple Degradation Processes Using Inverse Gaussian Process and Copulas (2014, background): “[19] R. B. Nelsen, An Introduction to Copulas, Springer, New York, NY, USA, 2nd edition, 2006.”
Modeling International Financial Returns with a Multivariate Regime Switching Copula (2009, neutral): “4A more detailed account of copulas can be found in Joe (1997), Nelsen (1999) and in Cherubini, Luciano & Vecchiato (2004) who provide a more finance-oriented presentation.”
Large‐sample tests of extreme‐value dependence for multivariate copulas (2011, neutral): “It is well-known (see e.g., Nelsen, 2006, Theorem 2.2.7) that C[j] exists almost everywhere on [0,1]d and that, for those u∈[0, 1]d for which it exists, 0 ≤ C[j](u) ≤ 1.”
Copulas for finance (2000, positive): “Definition 1 (Nelsen (1998), page 39) 1A N -dimensional copula is a function C with the following properties2: 1The original definition given by Sklar [1959] is (in french) Nous appelerons copule (à n dimensions) tout fonction C continue et non-décroissante — au sens employé pour une fonction de…”
A statistical framework for neuroimaging data analysis based on mutual information estimated via a gaussian copula (2016, background): “A copula [Nelsen, 2007] is a statistical structure that expresses the relationship between two random variables, independently of their marginal distributions.”
TAILS OF COPULAS (2013, neutral): “2013 casualty actuarial society CAS journal 2013d01 [7] 09-23-03 12:14 pm”
Sequential Monte Carlo on large binary sampling spaces (2011, neutral): “There have been earlier attempts to sample binary vectors via copulae: Lee (1993) describes how to construct an Archimedean copula, more precisely the Frank family (Nelsen, 2006, p.119), for sampling multivariate binary data.”
Non-Parametric Pricing of Multivariate Contingent Claims (2003, neutral): “A technique to price contingent claims can be developed using non-parametrically estimated marginal risk-neutral densities (based on options data) and a non-parametric dependence function (based on historical return data).”