1. Parameterising Copulas Staple Inn Thursday, 16 th November 2006

2. Outline  Outline & Introductions  The Smith Institute  The Warm-up Act  Maths and Graphs  An Academic Interlude  Parameterising Copulas  Q&A and Party Bags  Drinks & Nibbles

3. Outline  Outline & Introductions  The Smith Institute  The Warm-up Act  Maths and Graphs  An Academic Interlude  Parameterising Copulas  Q&A and Party Bags  Drinks & Nibbles James Orr Trevor Maynard Andreas Tsanakas David Allwright James & Trevor 5 mins 15 mins 20 mins 10 mins Robert Leese 10 mins James et al 15 mins

4. Multiple Choice  Question paper was on your seat  To help capture some of tonight’s key points  To encourage you to pay attention  The answers are on the copulas wiki  the link is on the back page of the question paper  No prizes for getting them all right  just a moment of “actuarial smugness”

5. Example Data Set

6. Warm Up James Orr Chair of Research Steering Committee

7. Dependency Modelling - Motivation  Risk of simultaneous asset movements  Risk of aggregate losses across business lines  Common source of “extreme” events  Key to ICAS and Economic Capital calculations  Systemic effects drive overall performance  It’s easier to cope with one thing at a time

8. Dependency Modelling - Spectrum Complexity Causal Factor Gas Laws Newtonian Mechanics Thermodynamics GCMs Econometrics Catastrophe Models GLMs ESGs Mortality Options Pricing Wilkie Model Annuitants Insureds Pensioners

9. Causal Mechanism Example 1.We’ll pick a letter of the alphabet “  ” 2.How often does “  ” appear in your first name?  Call this x i (as you’re the ith delegate) 3.How often does “  ” appear in your second name?  Call this y i 4.On our cue  Clap x i times  Stamp y i times

10. Our First Selected Letter  A consonant h  After 3… 11 22 33

11. Our Second Selected Letter  A consonant r  After 3… 11 22 33

12. Let’s look at our original data

14. Our Third Selected Letter  A vowel e  After 3… 11 22 33

15. Our Final Selected Letter  A vowel a  After 3… 11 22 33

16. Finally, let’s unpick the data a little

17. How did X & Y relate?