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
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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