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#5




A variable annuity has the following guarantees:
Guaranteed minimum death benefit with a return of premium guarantee. Guaranteed minimum accumulation benefit with a return of premium guarantee, effective 10 years from the date the policy is sold. Earningsenhanced death benefit that pays the beneficiary an additional benefit equal to 20% of any increase in the account value. P(T) denotes the value of a Euro put option on the annuity value, with the strike price equal to the original amount invested and tie to expiration T. A) C(t)f(t)dt+Pr(T>=10)*P(10)+0.2*C(t)f(t)dt C) P(t)f(t)dt+Pr(T>=10)*P(10)+0.2*C(t)f(t)dt 
#6




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Let K be in the initial amount invested and S_T be the account value at time T when the policyholder dies. The beneficiary receives the larger of the two values at time T, max(S_T, K), which can be rewritten as: max(S_T, K) = S_T + max(0, K  S_T) Without any guarantee, observe the beneficiary would simply receive S_T. Thus, the additional value of this guarantee is max(0, K  S_T), which is the payoff of a European put option. That's why the value of the guarantee is the value of this put option (not call option), and thus we should have P(t) (not C(t)) in the first term. 
#7




Bye the way, the question is from question 39 from the official IFM sample question.
I understand why it forms the payoff of a put option. My question is that can it also form the payoff of a call option because max(S_T, K) can also be K + (S_T  K, 0). Question 37 from the official IFM sample question uses this. The reason that question 37 can use the payoff of a call is that it did not state return of premium guarantee? Moreover, shouldn't the answer of question 39 also have S_T? The answer I think is S_T + P(t)f(t)dt + Pr(T>=10)*P(10) + 0.2*C(t)f(t)dt. 
#8




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