Lecture

Copulas: Properties and Applications

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In course

FIN-417: Quantitative financial risk management

This course is an introduction to quantitative risk management that covers standard statistical methods, multivariate models, risk measures, non-linear dependence structures (copula models), as well as credit risk. ...

Description

This lecture introduces copulas, which are distribution functions on [0, 1] with standard uniform marginal distributions. It covers the properties of copulas, such as the rectangle inequality and invariance under strictly increasing transformations. The lecture also discusses Sklar's Theorem, which shows the implicit use of copulas in multivariate distributions. Furthermore, it explores the concept of meta distributions, Gaussian copulas, and various dependence measures like linear correlation, rank correlations (Kendall's tau and Spearman's rho), and coefficients of tail dependence. The lecture concludes with a discussion on fallacies related to rank correlations and the parametrization of copulas.

Instructors (2)

Semyon Malamud

Teaching & PhD PhD Students Johannes Schwab, Onur Demiray, Giuseppe Matera Past EPFL PhD Students Rémy Praz, Evgeny Petrov, Yuan Zhang, Julien Arsène Blatt, Erik Hapnes, Teng Andrea Xu, Boris Kuznetsov Courses Big Data and Machine Learning for Financial Economics FIN-622 This class is an introduction to Machine Learning and High Dimensional Statistics in Finance. We start with purely empirical approach, focusing first on high dimensional regressions then moving to kernel methods and deep l

Damir Filipovic

Damir Filipovic holds the Swissquote Chair in Quantitative Finance and is Swiss Finance Institute Professor at the Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland. Prior to this, he was head of the Vienna Institute of Finance and professor at the University of Vienna. He previously held the chair of financial and insurance mathematics at the University of Munich, and he was on the faculty of Princeton University. He received his Ph.D. in mathematics from ETH Zurich in 2000. Damir Filipovic worked as a scientific consultant for the Swiss Federal Office of Private Insurance from 2003 to 2004. There he co-developed the Swiss Solvency Test, which defines the regulatory capital requirement for all Swiss based insurance companies and groups. He is on the editorial board of several academic journals. His research interests include the term structure of interest rates, credit and volatility risk, quantitative methods in risk management, and stochastic processes. His papers have been published in a variety of academic journals including the Journal of Financial Economics, Mathematical Finance, Finance and Stochastics, and the Annals of Applied Probability. He is the author of a textbook titled Term-Structure Models.

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (32)

Copula (probability theory)

In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval [0, 1]. Copulas are used to describe/model the dependence (inter-correlation) between random variables. Their name, introduced by applied mathematician Abe Sklar in 1959, comes from the Latin for "link" or "tie", similar but unrelated to grammatical copulas in linguistics.

Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.

Correlation

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.

Normal distribution

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.

Rank correlation

In statistics, a rank correlation is any of several statistics that measure an ordinal association—the relationship between rankings of different ordinal variables or different rankings of the same variable, where a "ranking" is the assignment of the ordering labels "first", "second", "third", etc. to different observations of a particular variable. A rank correlation coefficient measures the degree of similarity between two rankings, and can be used to assess the significance of the relation between them.

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