SOA Exam FAM Sample Question 104
Study guide: Exam FAM
An insurer offers a three-year contract with a guaranteed minimum of the policyholder's original investment.
You are given:
(i) The policyholder invests a premium of 1000.
(ii) The insurer keeps 2.5% of the premium to cover expenses, then invests the remainder in a mutual fund.
(iii) The mutual fund investment value follows the lognormal distribution with parameters \mu = 0.075 and \sigma = 0.15 per year.
(iv) The continuously compounded risk-free rate of interest is 6.5%.
(v) The mutual fund does not pay dividends.
Calculate the probability that the insurer's guarantee applies at the maturity date.
- A) 0.165
- B) 0.181
- C) 0.193
- D) 0.221
- E) 0.257
Answer this question and see the worked solution