4. (9 points) LifeCo wants to modify the design of its Equity Linked GIC product to reduce
the impact of a large decline in the stock market just before maturity. LifeCo believes
that these modifications should be done in such a way that the participation rate is as high
as possible and the profit margin remains the same.
The Company is also concerned about the cost of purchasing call options for the Equity
Linked GICs and is considering applying the dynamic hedging program it developed for
its Variable Annuities.
(a) Compare the options embedded in LifeCo’s Equity Linked GIC and Variable
Annuities.
(b) Recommend potential changes to the Equity Linked GIC product that would meet
LifeCo’s goals for the redesigned product.
(c) Describe the process used to evaluate the cost and efficiency of dynamic hedging.
(d) Evaluate LifeCo’s Variable Annuity dynamic hedging program as an alternative
to purchasing call options for its Equity Linked GIC product.
(e) Contrast the hedging of Equity Linked GICs as a stand-alone product to that of an
investment option of a Variable Universal Life product.
COURSE 8: Fall 2004 -5- GO ON TO NEXT PAGE
Investment
Morning Session
5. (8 points) You are constructing a model that will be used for dynamically hedging the
guaranteed minimum death benefits (GMDB) on a variable annuity portfolio. The
following models have been proposed:
(i) Lognormal
(ii) Regime Switching
(iii) Time Series Model with GARCH Volatility
(iv) Empirical
(v) Wilkie
(vi) Stable Distribution
(a) (3 points) Evaluate each model for modeling equity returns.
(b) (5 points) Assess the suitability of each model for dynamic hedging and
recommend a model to be used for dynamically hedging the GMDB.
COURSE 8: Fall 2004 -6- GO ON TO NEXT PAGE
Investment
Morning Session
6. (7 points) ABC Life has issued a 2-year GIC that has no policyholder options and pays
interest at maturity.
Single Premium 100 million
Payout in 2 years 110 million
Initial Assets (MV) 100 million of 3-year zero coupon corporate bonds
Treasury zero-coupon rates
Term, Years
Year 1 2 3
0 3% 4% 5%
1 4% 4% 4%
2 3% 4% 5%
Bond Spread Curve
1 year 2 year Corporate bond 3 year
spreads 0.1% 0.3% 0.5%
Assume:
•the bond spread curve does not change from issue
•expenses are negligible
•GIC issues occur at the beginning of the year
•payouts occur at the end of the year
(a) Compute the Total Returns in year 1 for both assets and liabilities using the Total
Return Approach.
(b) Disaggregate the Total Returns into their components, e.g. C-risks.
(c) Outline the advantages of the Total Return Approach over the book-value
approach.
COURSE 8: Fall 2004 -7- GO ON TO NEXT PAGE
Investment
Morning Session
Daily return distribution
0 1 0 1 0 2 4 5
15
33
52
65
40
19
9
4 2 1 1 0 0
0
10
20
30
40
50
60
70
-5.00%
-4.50%
-4.00%
-3.50%
-3.00%
-2.50%
-2.00%
-1.50%
-1.00%
-0.50%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
4.50%
5.00%
Daily return
Number of days

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