Introduction to Copulas

Name: Introduction to Copulas
Rating: 4.5 (125 reviews)

By MJ the Fellow Actuary

Last updated 7/2022

English

English [Auto],

What you'll learn

2 sections • 12 lectures • 1h 4m total length

Introduction to Copulas12:47
Examine copulas as mathematical objects that transform marginals into a joint distribution using generator functions and their inverses, illustrating independent, Gumbel, and normal copulas.
Sklar's Theorem2:08
Sklar's theorem asserts that a joint cumulative distribution function F_{X,Y} can be expressed through marginal CDFs F_X and F_Y via a copula, with uniqueness when F_X and F_Y are continuous.
Survival Copula1:18
Explore survival copulas, linking marginal survival functions to a joint survival function, and show copulas need not be limited to cumulative distribution functions.
Frechet and Hoeffding Boundary Copulas7:26
Correction*
Minimum Copula is Upper Bound.
Maximum Copula is Lower Bound.
Archimedean Copulas6:23
Gumbel Copula4:20
Explore the Gumbel copula, its generator-based construction, and how the alpha parameter governs upper tail dependence, illustrating credit portfolio risk in extreme value contexts.
Frank Copula3:06
Explore the frank copula, a generator-based copula with an alpha parameter. It has no upper or lower tail dependency, and extreme alpha values yield maximum or minimum copulas.
Clayton Copula3:37
Explore the Clayton copula and its two-parameter generator with alpha and beta, including alpha=1 reducing to the gumballs copula and beta=0 yielding tail dependencies.
Gaussian and Student t Copula5:25

Question 16:49
Question 23:45
List the copulas—Gumbel, Frank, Clayton, and Generalized Clayton—and explain when to use each, with losses, stock-bond returns, stock portfolios, and collectible car values as examples.
Question 36:58
Explores four-dimensional copula modeling with alpha equals 2.5 to verify the probability of no losses exceeding 95 percent under a value-at-risk framework, and discusses capital needs, regulatory and model risk.

This course is designed primarily for Actuarial Students writing exam SP9 and CS2.

The focus of these videos is on the theory rather than the application.

We look at the following

We focus on the generator functions and the dependency structure.

We don't look at any R code or real life applications.