Introductory reading on Copulas

For some time now, I have been looking for a good introductory reading on Copulas for my seminar. I am finding lots of material that talk about theoretical aspects, which is good, but before I move onto them I am looking to build a good intuitive understanding on the topic.

Could anyone suggest any good papers that provide a good foundation to a beginner (I have had 1-2 courses in statistics and understand marginals, multi-variate distributions, inverse transform, etc., to a reasonable extent)?

• The Joy of Copulas is a pretty good place to start. There are also several questions and answers that discuss some aspects of them here. The main thing to realize is than "copula" is just a fancy word for "multivariate distribution on the unit hypercube with uniform marginal distributions". It's also faster to say. Commented Sep 25, 2012 at 10:29
– Yoda
Commented Sep 25, 2012 at 15:32
• @Yoda: I think NaN looks for something less theoretical as a first reading. I would instead suggest google.be/… Commented Sep 25, 2012 at 15:47
• @Yoda: (+1) That is an excellent first introduction to the theoretical aspects. It is "the" standard book. Commented Sep 25, 2012 at 16:35
• @ocram: (+1) That is another good introduction that I meant to mention by the same author as the article I alluded to in the first comment: C. Genest and J. MacKay (1986), The Joy of Copulas: Bivariate Distributions with Uniform Marginals, The American Statistician, vol. 40, no. 4, pp. 280-283. Commented Sep 25, 2012 at 16:37

A concise introduction is T. Schmidt 2008 - Copulas and dependent measurement. Also noteworthy is Embrechts 2009 - Copulas - A personal view.

For Schmidt I could not provide a better summary than the section titles. It provides basic definitions, intuition and examples. Discussion of sampling is bare-bone, and a brief literature review covers the must-have. As for Embrechts apart from the obligatory definitions, properties and examples the discussion is interesting since it touches drawbacks and some critical remarks made to copula modeling over the years. The bibliography is here more extensive and covers most works that one shall read

Chris Genest has another introductory paper "Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask".

• Can you provide a brief summary of this paper?
– chl
Commented Jul 10, 2013 at 7:36

A good layperson introduction to copulas and its use in quantative fianance is

http://archive.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=all

The concept of correlation of probabilities is illustrated by two elementary school students Alice and Britney. It also discusses how prices of credit default swaps are used as a shortcut to the traditional rating process, as well as dangers of linking all of these together.

I recommend this paper as a must read: Li, David X. "On default correlation: A copula function approach." The Journal of Fixed Income 9.4 (2000): 43-54. Here's the PDF. It explains what copula is and how it can be used in the financial application. It's a nice easy read.

This should be followed by an article By Felix Salmon "Recipe for Disaster: The Formula That Killed Wall Street". Here how it starts:

A year ago, it was hardly unthinkable that a math wizard like David X. Li might someday earn a Nobel Prize. After all, financial economists—even Wall Street quants—have received the Nobel in economics before, and Li's work on measuring risk has had more impact, more quickly, than previous Nobel Prize-winning contributions to the field. Today, though, as dazed bankers, politicians, regulators, and investors survey the wreckage of the biggest financial meltdown since the Great Depression, Li is probably thankful he still has a job in finance at all. Not that his achievement should be dismissed. He took a notoriously tough nut—determining correlation, or how seemingly disparate events are related—and cracked it wide open with a simple and elegant mathematical formula, one that would become ubiquitous in finance worldwide.

Copulas are used to recover the joint probability function when only marginals are observed or available. One problem is that the joint probability may not be static, which seems to be the case with their use in default risk estimation. These two readings demonstrate that. Copulas worked fine in insurance, where the joint is very stable, such as death rate of spouses.

Another good introduction is An introduction to copulas (Nelsen 2006).

• Can you provide a brief summary of this book?
– chl
Commented Jan 29, 2015 at 20:09