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Potatowpn · 2020年08月11日

问一道题：NO.PZ2020011901000032

  1. FRM I
  2. Financial Markets And Products

问题如下：

What is the minimum USD annual premium that an insurance company should charge for a two-year term life insurance policy with face value of USD 1 million when the policyholder is a woman aged 71? (Use Table 2.1 and assume an interest rate of 3% compounded annually.)


选项：

A.

18,153

B.

17,874

C.

17,996

D.

17,767

解释：

B.

The probability of a payout in the first year (time 0.5 years) is 0.017275. The probability of a payout in the second year (time 1.5 years) is

(1 - 0.017275) * 0.019047 = 0.018718

The PV of the expected cost of the policy is therefore:

17,275/(1.030.5)+18,718/(1.031.5)=34,92817,275/(1.03^{0.5}) + 18,718/(1.03^{1.5}) = 34,928

The first premium is at time zero. The second premium, at time one year, has a probability of 1 - 0.017275 = 0.982725 of being made. If the premium is X, the expected present value is

X + 0.982725X/1.03 = 1.954102X

The minimum premium is given by solving:

1.954102X = 34,928

It is 17,874.

老师，请问这里为什么The probability of a payout in the first year用time 0.5 years不是1 year 、The probability of a payout in the second year 是time 1.5 years不是2years？

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1 个答案

小刘_品职助教 · 2020年08月11日

同学你好，

这道题是在预估一个现金流发生的时间，在1年之内发生payout的概率是0.017275，发生的时间点其实是假设在0.5这个时间点，而不是在1年末这个点。

水瓶公主 · 2023年03月14日

为什么赔偿是在年中，而不是年末

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