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1. Introduction
2. The Perfect Storm
3. From extremes to copulas
4. Correlation issues
5. Correlation issues: data clouds
6. Some real data: BMW and Siemens
7. Summary
8. Simulating random variables
9. Definition of a copula
10. Introducting Skar's theorem
11. Skar's theorem
12. Practical use of Skar's theorem
13. Generating copulas
14. Copulas and ranks
15. Standard families: Gaussian and t copulas
16. Other copula examples
17. Revisiting the data clouds
18. BMW's and Siemens's data revisited
19. Maurice Frechet and Wasilly Hoeffding
20. Frechet-Hoeffding bounds
21. Implications of Hoeffding theorem
22. An example for Hoeffding theorem
23. Implications of the example
24. Alternative correlation measures
25. Linear correlation revisited
26. An application to credit risk
27. A simulation example (1)
28. A simulation example (2)
29. Tail dependence
30. Tail dependence index
31. Tail dependence index: properties
32. Joint tail probabilities
33. Warning notice!
34. Bounds on risk measures
35. An appraisal of copulas
36. Back to BMW's and Siemens's data
37. Copula craze
38. Critical comments by Thomas Mikosch
39. Copulas: how we view them
40. Copula literature
41. Postcriptum

Topics Covered

• Impact of extremes and dependence in finance and insurance
• Correlation issues
• Copulas and Sklar's theorem
• Copula generation
• Frechet-Hoeffding bounds
• Limitations of correlation
• Rank correlation measures
• An application to credit risk
• Tail dependence
• Bounds on risk measures
• Critical appraisal

Links

Series:

• Quantitative Financial Risk Management

Categories:

• Finance, Accounting & Economics

Talk Citation

Publication History

• Published on October 1, 2007
• Archived on April 4, 2022