Cooljas · 2022年11月02日
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:
If the 1.5-year zero rate is R we must have:
The solution to this equation is R = 0.05027. The 1.5-year zero rate is therefore 5.027%.
品职答疑小助手雍 · 2022年11月03日
同学你好，我先回答后一问，这里就是用的复利折现啊，只不过不是连续复利，其实frm的计算中，我还是听习惯用复利，而不是连续复利的，不过通常结果差别不大。
然后本题zero rate也就是spot rate指的是某个特定期限的现金流对应的利率，所以根据本题给的条件，半年期的spot rate是3%，1年期的是4%。
现在给你了一个1.5年期债券的YTM，让你求1.5年期的spot rate。
首先可以根据YTM算出债券的价值，根据coupon和面值， 用YTM折现，算出来是98.572。
然后用spot rate则是对单个期限的现金流分别折现，也要得到98.572这个结果才行，这式子里只有1.5年的折现率是未知数，可以解出来1.5年spot rate是5.027%。
如果不了解coupon rate， spot rate（zero rate）的定义的话，我就真的没办法了，定义介绍我打字还不如百度，当然我建议方便理解的话去看基础班。
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
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。
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%.否则就直接100/（1+R）^1.5=P，求出R
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%.麻烦介绍下该类题型怎么做？谢谢
