1. Valuation and Capital: Segregated Fund Guarantees
Workshop on Options in Financial Products
Fields Institute – December 8, 2000
Allan Brender, OSFI

2. Actuarial Valuation of Liabilities
The object of valuation of actuarial liabilities is not to determine a market price.
Provision sufficient to meet policy liabilities
Cash flows contingent upon uncertain future events over a long term
Assumptions about the future include margins for adverse deviations

3. Actuarial Valuation of Liabilities
Actuarial liabilities represent an apportionment of the company’s assets required to satisfy obligations to policyholders.
Assets are segmented to back specific portfolios of business.
Insurers’ investment policy is long term, buy and hold, and built around ALM.

4. Actuarial Valuation of Liabilities
Policy cash flows are discounted at the yield earned on the supporting asset portfolio, or
The actuarial liability is equal to the statement value of the supporting asset portfolio.

5. Actuarial Valuation of Liabilities
Why not use market interest rates?
With market interest rates, separate provision would be required for asset/liability mismatch.
When insurance portfolios do trade, the trade usually involves transfer of the supporting asset portfolio.

6. Actuarial Valuation of Liabilities
Based upon projection of all relevant cash flows
Use a variety of economic scenarios
Policy cash flows may be sensitive to the economic scenario
Requires dynamic investment policy

7. Actuarial Valuation of Liabilities
Assume economic scenarios are generated stochastically.
We obtain a distribution of the cost of meeting obligations to policyholders.
We use this distribution to determine both the valuation of the liability and required capital.

8. Actuarial Valuation of Liabilities
How do we allow for economic uncertainty in the liability valuation ?
Use the risk-neutral (Q) measure and set the liability value equal to the mean, or
Use the ‘realistic’ (P) measure and set the liability value at some point in excess of the mean.
Actuaries choose this approach

9. Segregated Fund Guarantees
Individual seg fund product is similar to a mutual fund.
A seg fund is required when the return to the policyholder is directly related to a specific block of assets (ICA).
Guarantees of return of at least 75% of premiums upon death or maturity are required by provincial securities laws.

10. Segregated Fund Guarantees
OSFI requires (1971)
Guarantees not to exceed 100% of gross premiums (investments)
Maturity period of at least 10 years
Liabilities for seg fund guarantees to be established in an insurer’s general fund

11. Segregated Fund Guarantees
Initially, all seg funds carried 75% guarantees and maturities at a high (retirement) age.
In the mid-1980’s, one large insurer moved to 100% guarantees.
In the mid-1990’s, the market heated up, offering 10 year maturity periods and resets.

12. Segregated Fund Guarantees
In the mid and late 1990’s, we had
low policy liabilities
no capital requirement
for these guarantees
in spite of
results of the U.K. Maturity Guarantees Working Party
unfolding experience in Japan

13. Segregated Fund Guarantees
OSFI and the Canadian Institute of Actuaries (CIA) both expressed concern over the situation.
In 2000, the CIA’s Task Force on Segregated Fund Guarantees developed an approach to liability valuation and required capital.

14. Segregated Fund Guarantees
The Task Force’s approach is through projection of cash flows under stochastically generated scenarios, to generate the distribution of costs of these guarantees.
The resulting distribution is strange – ‘all tail’ with a large probability mass at 0.

15. Segregated Fund Guarantees
The Task Force considered a variety of economic models.
Not wishing to choose among them, the Task Force developed calibration criteria for the various models to ensure reasonably thick tails.

16. Calibration – Maximum Returns
Accumulation Period
2.5 percentile
5.0 percentile
10.0 percentile
1-year
0.76
0.82
0.90
5-year
0.75
0.85
1.05
10-year
1.35

17. Segregated Fund Guarantees
An interesting new model is the Regime Switching Lognormal Model developed by Prof. Mary Hardy of the University of Waterloo
Six parameters
Makes maximal use of calibration points

18. Segregated Fund Guarantees
Two levels are specified in the distribution
The first for the liability value
The second for the total of liabilities and required capital
Levels are specified in terms of the Conditional Tail Expectation at the xth percentile, CTE(x)

19. Capital Requirements
OSFI has selected CTE(95) for the total of liabilities and required capital.
Required capital is subject to the usual MCCSR multiplier.
There is a phase-in over
For 2000, required capital is to be determined through a factor-based formula.

20. Use of Internal Models
If internal models are used to determine capital requirements, these will be subject to a regime similar to that applied to banks’ models for determining capital for trading risk.
Audit of models by OSFI
Required risk management program with oversight by OSFI

21. Use of Internal Models
Credit for dynamic hedging requires modelling of the hedging activity.
The economic scenario generator will have an underlying P-measure.
It must incorporate a Q-measure generator to price hedges at future time points within any scenario.

22. Use of Internal Models
Credit for dynamic hedging requires modelling of the hedging activity.
Hedges will increase costs in all scenarios.
Hedge pay-offs in unfavourable scenarios will reduce costs.

23. Valuation and Capital: Segregated Fund Guarantees
Allan Brender