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This presentation is based on a part of an academic course on Enterprise Risk Management (ERM) titled ‘Correlation, co-dependency and risk aggregation’ and covers topics such as: the Central Limit Theorem (CLT), risk modelling using factor structures and copula based dependency structures

Slides

1	Session 7: Correlation, co-dependency and risk aggregation
2	Session 7: Correlation, co-dependency and risk aggregation
3	Introduction
4	Consider first multivariate Normal, i.e. Gaussian, case
5	MVaR in Gaussian Case
6	E.g. outcomes uncorrelated, equal weights
7	Session 7: Correlation, co-dependency and risk aggregation
8	Central Limit Theorem
9	CLT potentially applicable at two levels
10	CLT can break down in the following ways:
11	Mathematical axioms and No arbitrage principle
12	Session 7: Correlation, co-dependency and risk aggregation
13	Dependency (aka co-dependency/co-movement)
14	Factor structure - notation
15	Factor structure - handling idiosyncratic risk
16	Advantages of introducing a factor structure
17	Identifying factor structures - 3 main model types
18	Identifying factor structures in practice (1)
19	Identifying factor structures in practice (2)
20	Session 7: Correlation, co-dependency and risk aggregation
21	Illustrative distribution (two risk factors) (1)
22	Illustrative distribution (two risk factors) (2)
23	E.g. bivariate copula (1)
24	E.g. bivariate copula (2)
25	Copula and copula density
26	Copulas
27	Copulas and Sklar’s theorem
28	Example Copulas
29	Tail dependence
30	Interpretation of tail index
31	Gaussian and Independence copula
32	Simulating r.v.s linked by Gaussian copula
33	Simulations with non-Gaussian copulas
34	Fitting copulas empirically
35	Risk aggregation
36	Risk aggregation using copulas
37	Important Information

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