Tail fitting probability distributions for risk management purposes
This presentation describes:
- why the 'tail' behaviour of distributions of returns or losses is important (i.e. the magnitude of extreme outcomes),
- Traditional Extreme Value Theory (EVT) techniques that have previously been used to model such behaviour, and their strengths and weaknesses
- Some new refinements explained in the presentation and an attached paper allowing tail behaviour to be fitted using arbitrary distributional forms
- Other uses of such techniques, including 'quantile interpolation' for fast evaluation of risk measures such as Value-at-Risk.
[as
pdf]
Slides
1 | Tail fitting probability distributions for risk management purposes |
2 | Agenda |
3 | Agenda |
4 | Why is tail behaviour important? (1) |
5 | Why is tail behaviour important? (2) |
6 | Why is tail behaviour important? (3) |
7 | Agenda |
8 | Extreme Value Theory (EVT) |
9 | Traditional EVT results |
10 | But is EVT the only or best way of fitting the tail? |
11 | Potential weaknesses of EVT |
12 | Agenda |
13 | Tail-weighted distribution fitting |
14 | Tail weighted maximum likelihood (TWMLE) |
15 | Tail weighted least squares (TWLS) |
16 | Example analysis |
17 | Key takeaways |
18 | Agenda |
19 | Fitting distributions around specific quantiles |
20 | Quantile interpolation (1) |
21 | Quantile interpolation (2) |
22 | Quantile interpolation: Results (1) |
23 | Quantile interpolation: Results (2) |
24 | Summary |
25 | Appendix A: Visualising fat-tailed behaviour |
26 | Quantile-quantile plots: other comments |
27 | Quantile-quantile plots |
28 | More periods give more scope for extreme events |
29 | Appendix B: Time-varying volatility |
30 | Important Information |
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