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除了樱花 · 2022年04月08日

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  1. FRM I
  2. Financial Markets And Products

NO.PZ2020021204000012

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?

选项：

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+102（1+0.05/2）3=98.572\frac2{1+0.05/2}+\frac2{{(1+0.05/2)}^2}+\frac{102}{（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+102（1+R/2）3=98.572\frac2{1+0.03/2}+\frac2{{(1+0.04/2)}^2}+\frac{102}{（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%.

coupon等于2是自己设的吗？

这道题的解题思路是什么？

是利用bond yield = spot rate来求吗？

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品职答疑小助手雍 · 2022年04月08日

同学你好，这题问只要理解zero rate和YTM的定义就可以做题了。bond yield是YTM，spot rate即zero rate。

用spot rate和YTM套公式求出的price应该是一样的，根据本题的条件，两套公式里未知数只有1.5年期的spot rate。

除了樱花 · 2022年04月09日

face value100题目里没给啊，是自己假设的吗

品职答疑小助手雍 · 2022年04月09日

这个face value是多少都对结果没有影响的，本题只是拿100来进行计算了。

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NO.PZ2020021204000012问题如下The six-month anone-yezero rates are 3% an4% (both compounsemi-annually) ana 1.5-yebonpaying a coupon of 4% per annum semi-annually ha yielof 5%. Whis the 1.5-yezero-coupon interest rate? The priof the 1.5-yebonwith a favalue of 100 is:21+0.05/2+2(1+0.05/2)2+102（1+0.05/2）3=98.572\frac2{1+0.05/2}+\frac2{{(1+0.05/2)}^2}+\frac{102}{（1+0.05/2）^3}=98.5721+0.05/22​+(1+0.05/2)22​+（1+0.05/2）3102​=98.572If the 1.5-yezero rate is R we must have:21+0.03/2+2(1+0.04/2)2+102（1+R/2）3=98.572\frac2{1+0.03/2}+\frac2{{(1+0.04/2)}^2}+\frac{102}{（1+R/2）^3}=98.5721+0.03/22​+(1+0.04/2)22​+（1+R/2）3102​=98.572The solution to this equation is R = 0.05027. The 1.5-yezero rate is therefore 5.027%.同上，为什么这两个rate会是不同的

2024-05-19 21:48 1 · 回答

NO.PZ2020021204000012问题如下The six-month anone-yezero rates are 3% an4% (both compounsemi-annually) ana 1.5-yebonpaying a coupon of 4% per annum semi-annually ha yielof 5%. Whis the 1.5-yezero-coupon interest rate? The priof the 1.5-yebonwith a favalue of 100 is:21+0.05/2+2(1+0.05/2)2+102（1+0.05/2）3=98.572\frac2{1+0.05/2}+\frac2{{(1+0.05/2)}^2}+\frac{102}{（1+0.05/2）^3}=98.5721+0.05/22​+(1+0.05/2)22​+（1+0.05/2）3102​=98.572If the 1.5-yezero rate is R we must have:21+0.03/2+2(1+0.04/2)2+102（1+R/2）3=98.572\frac2{1+0.03/2}+\frac2{{(1+0.04/2)}^2}+\frac{102}{（1+R/2）^3}=98.5721+0.03/22​+(1+0.04/2)22​+（1+R/2）3102​=98.572The solution to this equation is R = 0.05027. The 1.5-yezero rate is therefore 5.027%.这题里面的Yiel有效年利率的意思吗？为什么债券的定价，每一次现金流都用这个yiel折现？谢谢。

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