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Infinite · 2020年02月19日

问一道题：NO.PZ2020021204000012

  1. FRM I
  2. Financial Markets And Products

问题如下：

The six-month and one-year zero rates are 3% and 4% (both compounded semi-annually) and a 1.5-year bond paying a coupon of 4% per annum semi-annually has a yield of 5%. What is the 1.5-year zero-coupon interest rate?

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解释：

The price of the 1.5-year bond with a face value of 100 is:

21+0.05/2+2(1+0.05/2)2+2(1+0.05/2)3=98.572\frac2{1+0.05/2}+\frac2{{(1+0.05/2)}^2}+\frac2{{(1+0.05/2)}^3}=98.572

If the 1.5-year zero rate is R we must have:

21+0.03/2+2(1+0.04/2)2+2(1+R/2)3=98.572\frac2{1+0.03/2}+\frac2{{(1+0.04/2)}^2}+\frac2{{(1+R/2)}^3}=98.572

The solution to this equation is R = 0.05027. The 1.5-year zero rate is therefore 5.027%.

答案里第二计算R的公式 分子用coupon=2,求1.5year的zero coupon rate不是期间没有现金流吗？为什么还用copon=2还求呢？

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1 个答案

品职答疑小助手雍 · 2020年02月20日

同学你好，这题考的是用spot rate和YTM求出的price应该是一样的，所以现金流按3,4，X，折现和5,5,5折现得到的price应该是一样的。

只是解析也有问题，第三期的现金流应该加上本金，应该是102。两个式子都只写了coupon

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