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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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