1. October 19-20, 2006 Chicago, Illinois
CIA General Meeting
October 19-20, 2006
Chicago, Illinois
Session IP-31

2. Stochastic Models: Application to LTD
When is a stochastic model appropriate?
Why stochastic LTD?
How?

3. Stochastic LTD Models Ideas presented are very Blue Sky
My goal to provoke thought
Not that hard to do
Excel model

4. When Are Stochastic Models Appropriate?
When the loss model has
a long or heavy right tail
A “cliff” or trigger point
Dependencies of Risk

5. Looking At LTD Models Traditionally viewed as a life annuity
We can also view these as a random variable with probability distribution

6. Why Not Look at LTD This Way?

7. Why Not Look at LTD This Way?
Heavy tail
Trigger Point

8. Why Use the Same Formula for These Loss Models?

9. Dependencies of Risks Between Claims
LTD Experience is influenced by
Economic conditions
Geographic location
CPP policy
Court decisions
Legislation
All of these lead to a dependency between claims

10. Dependencies of Risks Between Years
Relationship between incidence and termination rates
High incidence rates may mean more softer claims
Higher termination rates in subsequent years
Low incidence rate may mean “harder” claims
Cyclical termination rates
Claims clean up focuses on soft claims
Followed by period of low termination rates
High turnover in adjudicators leads to low terminations
Followed by period of high termination rates
This year’s experience influences next year’s experience

11. Simple Stochastic Model
1000 Trials
Each trial represents one possible outcome for the portfolio
For each trial
Simulate the time on claim for each life
Use CIA LTD table to determine distribution of time on claim
Sum the PVs for all lives

12. Test Case 1 500 lives from a real LTD block Mature block of claims
High female content

13. Test Case 1 Results Mature block of 500 claims Results fairly stable
Limited up side risk

14. Test Case 1 Results

15. Test Case 2 Subset of Test Case 1
100 lives within 2 years of disability
Representative of new LTD group

16. Test Case 2 Results
Note a 5% Pad indicates 95% of monthly termination rates
Results less stable (Smaller group, within Own Occ period, younger lives)

17. Test Case 2 Results

18. Does the law of large numbers apply?
Test Case 1 indicates that risk is greatly reduced in a large, mature block
Good experience offsets bad
But …
Cyclical nature of LTD means that all groups have bad years together
If we write refund LTD, we give the good experience back and keep the bad

19. Uses For Stochastic LTD Models
Supplement not replace deterministic models
Better understanding of risks
Stop loss and Durational Pooling charges
Refund LTD reserves

20. Accounting for Dependencies of Risks
Add a random variable
allow for good or poor years
affects all lives equally
key impact in early years
Modification to termination probability for each year
Autoregressive component for cycles?