tristabo · 2024年05月19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?
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%.
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
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%.
