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1. Introduction
2. Statistical models for risk management
3. Outline
4. Definisions of returns
5. Annualize multiyear returns
6. Log return and multiperiod return
7. Dividend paying assets
8. Excess return
9. Distribution of returns
10. Problems (1)
11. Problems (2)
12. Log-normal
13. Log-returns
14. Final equation
15. Basic definition of normal random variable
16. Finding all moments
17. Log-normal and historical returns
18. Returns - summary of stylized facts
19. Notation
20. Skewness and kurtosis - definition
21. Note
22. Autocovariance
23. Stationarity (1)
24. Stationarity (2)
25. Autocorrelation
26. Distributional model for asset return (1)
27. Distributional model for asset return (2)
28. Distributional model for asset return (3)
29. Models of conditional variance
30. ARCH/GARCH (1)
31. ARCH/GARCH - properties
32. ARCH/GARCH (2)
33. Stochastic volatility (SV) models (1)
34. Stochastic volatility (SV) models (2)
35. Distribution of returns - multivariate
36. Multivariate normal distribution
37. Note - multivariate normal distribution (1)
38. Note - multivariate normal distribution (2)
39. Mixture distributions (1)
40. Mixture distributions (2)
41. Mixture distributions (3)
42. Multivariate GARCH processes (1)
43. Multivariate GARCH processes (2)
44. Non-linear dependence and copulas
45. Note - non-linear dependence
46. Sklar's theorem (Sklar (1959)) (1)
47. Sklar's theorem (Sklar (1959)) (2)
48. Rank correlation, tail dependence and copulas (1)
49. Rank correlation, tail dependence and copulas (2)
50. Rank correlation, tail dependence and copulas (3)
51. Tail dependence
52. Copulas - types
53. Bivariate Gaussian copula (1)
54. Bivariate Gaussian copula (2)
55. t copula
56. Gumbel copula
57. Clayton copula
58. References and further reading (1)
59. References and further reading (2)
60. Further reading

Topics Covered

• Definition of returns: simple returns and log returns
• Distribution of returns, univariate: normal and log-normal distribution
• Stylized facts of historical returns
• Skewness, kurtosis, autocorrelation and stationarity
• ARCH, GARCH and stochastic volatility (SV) models
• Distribution of returns, multivariate: multivariate normal distribution
• Multivariate GARCH and SV models
• Copulas and non-linear dependence

Links

Series:

• Quantitative Financial Risk Management

Categories:

• Finance, Accounting & Economics

Talk Citation

Publication History

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