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Foundation ERM Session 7: Correlation, co-dependency and risk aggregation


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



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