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

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

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

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

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

Why Not Look at LTD This Way?

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

Why Use the Same Formula for These Loss Models?

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

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

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

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

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

Test Case 1 Results

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

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)

Test Case 2 Results

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

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

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?