9. An insurance company sell single premium?

9. An insurance company sells single premium deferred annuity contracts with return related to a stock index, the time-t value of one unit of which is denoted by S(t). The contracts submit a minimum guarantee return rate of 3%. At time 0, a single premium of amount P is paid by the policyholder, and P*y% is deducted by the insurance company. Thus, at parenthood (in one year), the insurance company will pay the policyholder:
P*(1 - y%)*Max[S(t)/S(0), 1.03]

You are given the following information:

(i) Ignore any consideration of dividend payments.
(ii) S(0) = 100.
(iii) The price of a one-year european put option, near strike price $103, on the stock index is $15.21.

Determine y%, so that the insurance company does not make or lose money on this contract.
Answers:
Do your own homework.

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