JK_MMMM · 2022年02月24日
NO.PZ2019052801000035
问题如下：
Assume that the annualized 6-month spot rate is 5.2%, the 1-year spot rate is unknown, both spots are continuously compounded rates. A $100 face value, 1-year, 6% semiannual bond is priced at $97.83. Calculate the 1-year spot rate:
选项：
A.7.63%
B.8.18%
C.9.21%
D.10.96%
解释：
B is correct.
考点：Interest Rate
解析：
annualized 6-month spot rate表示为 ,1-year spot rate
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NO.PZ2019052801000035问题如下Assume th the annualize6-month spot rate is 5.2%, the 1-yespot rate is unknown, both spots are continuously compounrates. A $100 favalue, 1-year, 6% semiannubonis price$97.83. Calculate the 1-yespot rate:A.7.63%B.8.18%C.9.21%10.96%B is correct. 考点Interest Rate解析annualize6-month spot rate表示为 Z1Z_1Z1,1-yespot rate Z2Z_2Z2B=3×e[(−Z1/2)×1]+103×e[(−Z2/2)×2]B=3\times e^{\lbrack{(-Z_1/2)}\times1\rbrack}+103\times e^{\lbrack{(-Z_2/2)}\times2\rbrack}B=3×e[(−Z1/2)×1]+103×e[(−Z2/2)×2];$97.83=3×e[(−0.052/2)×1]+103×e[(−Z2/2)×2]\$97.83=3\times e^{\lbrack{(-0.052/2)}\times1\rbrack}+103\times e^{\lbrack{(-Z_2/2)}\times2\rbrack}$97.83=3×e[(−0.052/2)×1]+103×e[(−Z2/2)×2];Z2=0.081832=8.18%Z_2=0.081832=8.18\%Z2=0.081832=8.18% 老师好，annulize6 month rate 5.2%，这个英文意思不是“年化的6个月利率”？我理解也就是把年化利率除以2了，难道不是这么理解吗？如果是年化利率不应该直接表达为“annulizerate”？如果是这样表达，我觉得6个月的利率应该是除以2的。
NO.PZ2019052801000035 问题如下 Assume th the annualize6-month spot rate is 5.2%, the 1-yespot rate is unknown, both spots are continuously compounrates. A $100 favalue, 1-year, 6% semiannubonis price$97.83. Calculate the 1-yespot rate: A.7.63% B.8.18% C.9.21% 10.96% B is correct. 考点Interest Rate解析annualize6-month spot rate表示为 Z1Z_1Z1,1-yespot rate Z2Z_2Z2B=3×e[(−Z1/2)×1]+103×e[(−Z2/2)×2]B=3\times e^{\lbrack{(-Z_1/2)}\times1\rbrack}+103\times e^{\lbrack{(-Z_2/2)}\times2\rbrack}B=3×e[(−Z1/2)×1]+103×e[(−Z2/2)×2];$97.83=3×e[(−0.052/2)×1]+103×e[(−Z2/2)×2]\$97.83=3\times e^{\lbrack{(-0.052/2)}\times1\rbrack}+103\times e^{\lbrack{(-Z_2/2)}\times2\rbrack}$97.83=3×e[(−0.052/2)×1]+103×e[(−Z2/2)×2];Z2=0.081832=8.18%Z_2=0.081832=8.18\%Z2=0.081832=8.18% 我列出算式了，但是计算器如何按呢？
NO.PZ2019052801000035 问题如下 Assume th the annualize6-month spot rate is 5.2%, the 1-yespot rate is unknown, both spots are continuously compounrates. A $100 favalue, 1-year, 6% semiannubonis price$97.83. Calculate the 1-yespot rate: A.7.63% B.8.18% C.9.21% 10.96% B is correct. 考点Interest Rate解析annualize6-month spot rate表示为 Z1Z_1Z1,1-yespot rate Z2Z_2Z2B=3×e[(−Z1/2)×1]+103×e[(−Z2/2)×2]B=3\times e^{\lbrack{(-Z_1/2)}\times1\rbrack}+103\times e^{\lbrack{(-Z_2/2)}\times2\rbrack}B=3×e[(−Z1/2)×1]+103×e[(−Z2/2)×2];$97.83=3×e[(−0.052/2)×1]+103×e[(−Z2/2)×2]\$97.83=3\times e^{\lbrack{(-0.052/2)}\times1\rbrack}+103\times e^{\lbrack{(-Z_2/2)}\times2\rbrack}$97.83=3×e[(−0.052/2)×1]+103×e[(−Z2/2)×2];Z2=0.081832=8.18%Z_2=0.081832=8.18\%Z2=0.081832=8.18% 这里的N为什么不是0.5，1？
NO.PZ2019052801000035问题如下Assume th the annualize6-month spot rate is 5.2%, the 1-yespot rate is unknown, both spots are continuously compounrates. A $100 favalue, 1-year, 6% semiannubonis price$97.83. Calculate the 1-yespot rate: A.7.63% B.8.18% C.9.21% 10.96%B is correct. 考点Interest Rate解析annualize6-month spot rate表示为 Z1Z_1Z1,1-yespot rate Z2Z_2Z2B=3×e[(−Z1/2)×1]+103×e[(−Z2/2)×2]B=3\times e^{\lbrack{(-Z_1/2)}\times1\rbrack}+103\times e^{\lbrack{(-Z_2/2)}\times2\rbrack}B=3×e[(−Z1/2)×1]+103×e[(−Z2/2)×2];$97.83=3×e[(−0.052/2)×1]+103×e[(−Z2/2)×2]\$97.83=3\times e^{\lbrack{(-0.052/2)}\times1\rbrack}+103\times e^{\lbrack{(-Z_2/2)}\times2\rbrack}$97.83=3×e[(−0.052/2)×1]+103×e[(−Z2/2)×2];Z2=0.081832=8.18%Z_2=0.081832=8.18\%Z2=0.081832=8.18% 为什么答案里coupon直接等于三了，题目里没给啊
