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April 2013 Question 4 solution

D

dChetty

Member
The solution says

If the guaranteed annuity options are "in the money" then there is a risk of lower withdrawals prior to exercise date than allowed for in the pricing. If there guaranteed annuity options are "out of the money" then there is a risk of higher than expected withdrawals prior to exercise. Why would there be withdrawals? If it's in the money then the policyholder is getting a higher rate than in the market so he/she will not withdraw, am I right?

Why is a call option used here?

The solution also says. The company would need to determine an estimate for the proportion of policyholders taking the option at each age in order to derive the appropriate mix of terms of option on which to base the pricing. Is this referring to the take up rates at each age to determine the expected life expectancy at that age?
 
dChetty said:
The solution says

If the guaranteed annuity options are "in the money" then there is a risk of lower withdrawals prior to exercise date than allowed for in the pricing. If there guaranteed annuity options are "out of the money" then there is a risk of higher than expected withdrawals prior to exercise. Why would there be withdrawals? If it's in the money then the policyholder is getting a higher rate than in the market so he/she will not withdraw, am I right?
Click to expand...

Policyholders do not always choose the most expensive option. For example, a policyholder may prefer to have cash now even if a guaranteed annuity has higher actuarial value.

Also, policyholders are unlikely to have sufficient knowledge to assess which option is most valuable.

Mark
 
dChetty said:
The solution says


Why is a call option used here?
Click to expand...

A guaranteed annuity option could be backed by call options on a bond that would back the guarantee. If the policyholder exercises the guarantee we could exercise the option. If the policyholder does not exercise, then we have no need to buy the bond.

Mark
 
dChetty said:
The solution also says. The company would need to determine an estimate for the proportion of policyholders taking the option at each age in order to derive the appropriate mix of terms of option on which to base the pricing. Is this referring to the take up rates at each age to determine the expected life expectancy at that age?
Click to expand...

We'll need to know how many people exercise at each age and their life expectancy.

Mark
 
To ensure we get the income stream we need to pay the annuity
 
Is it a call option to protect against downward market movements in interest rates?
 
dChetty said:
Is it a call option to protect against downward market movements in interest rates?
Click to expand...

Yes. If interest rates go down, the price of the bond goes up, making the call option more valuable.

But I would think of it more as:
1. A call option on a bond is the option to purchase the bond at a specified price at a specified future date
2. Annuities are backed by bonds

So if the insurer purchases a call option and the policyholder exercises the GAO, then the insurer can exercise the option and back the annuity with the bond.
 
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