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magickame · 2021年10月18日

能否画个图？

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2019070101000039

问题如下：

The current 1-year spot rate = 5%, the 1-year forward rate one year from today is 6.65%, the 1-year forward rate two years from today = 7.82%, 1-year forward rate three years from today is 8.45%. What's the price of a 4-year bond？The bond has a par value of 100 and has a coupon rate of 8% paid annually.

选项：

A.

$101.211.

B.

$98.987.

C.

$103.875.

D.

$105.245.

解释：

C is correct

考点：Forward Rate 计算

解析：

先计算spot rate：

S1=5%

S2=[(1.05)(1.0665)]1/2-1=5.82%

S3=[(1.05)(1.0665)(1.0782)]1/3-1=6.48%

S4=[(1.05)(1.0665)(1.0782)(1.0845)]1/4-1=6.97%

第二步，计算债券价格

P=$81.05+$81.05822+$81.06483+$1081.06974=$103.875\text{P=}\frac{\$8}{1.05}+\frac{\$8}{1.0582^2}+\frac{\$8}{1.0648^3}+\frac{\$108}{1.0697^4}=\$103.875

Forward rate对应的具体位置还是有点模糊，视频里是往回倒推1期，还是麻烦画个图看的清楚点

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1 个答案

DD仔_品职助教 · 2021年10月18日

嗨，爱思考的PZer你好：


具体计算如下图，主要还是题目里对forward rate的描述需要搞清楚，才能知道在图形里面对应的是哪一段的利率

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