12345678wdv · 2024年03月10日
NO.PZ2019052801000049
问题如下：
A bank entered into a swap with two years to maturity as a floating rate payer. The fixed rate is 4%, with annal payments. The notional priciple is $5,000,000. The spot interest rates are as follows: one year, 3.5%; two years, 4.5%. Today is the reset day, the current value of the swap is closest to:
选项：
A.$54,437.
B.$-54,437.
C.-$30,125.
D.$30,125.
解释：
B is correct.
考点：利率互换估值.
解析：
支浮动的一方可以看作一个浮动利率债券，浮动利率债券在reset day 价值回归面值。
收固定的一方可以看作一个固定利率债券，
pzqa39 · 2024年03月10日
嗨，爱思考的PZer你好：
解题思路是swap就相当于两个债券，一个浮动一个固定。
Bfix算的是固定端每1块钱的面值对应的现值是多少。
浮动端题目中说Today is the reset day, 所以 value = principle，一块钱面值现值就是1块钱，
所以算好了Bfix减去1就等于1块钱swap的面值对应的swap现值。
乘以swap面值5million就得到swap的价值了。
所以收取固定利息部分的Bfix = 每期利息0.04*exp(-3.5%) + 期末本息之和1.04*exp(-4.5%*2) = 0.989113.
这个结果表示1美元的本金对应的收取固定利息部分的现值是0.989113美元。
利率互换的浮动利息部分的价值在reset date（题干末尾告诉我们的）一定是1，所以最后直接用0.989113-1，再乘以面值5million即可。
----------------------------------------------就算太阳没有迎着我们而来，我们正在朝着它而去，加油！
NO.PZ2019052801000049 问题如下 A bank entereinto a swwith two years to maturity a floating rate payer. The fixerate is 4%, with annpayments. The notionpriciple is $5,000,000. The spot interest rates are follows: one year, 3.5%; two years, 4.5%. Toy is the reset y, the current value of the sw is closest to: A.$54,437. B.$-54,437. C.-$30,125. $30,125. B is correct.考点利率互换估值.解析支浮动的一方可以看作一个浮动利率债券，浮动利率债券在reset y 价值回归面值。收固定的一方可以看作一个固定利率债券，Bfix =0.04e−0.035+1.04e−0.045×2=0.989113B_{fix}\;=0.04e^{-0.035}+1.04e^{-0.045\times2}\\=0.989113Bfix=0.04e−0.035+1.04e−0.045×2=0.989113lV=(0.989113−1)×5,000,000=−54,437{l}\\V=(0.989113-1)\times5,000,000=-54,437lV=(0.989113−1)×5,000,000=−54,437 比如，本题是floating payer，最终是用计算出的fix现金流的现值-面值1，为什么不是用1-fix现值呢，谢谢
NO.PZ2019052801000049问题如下A bank entereinto a swwith two years to maturity a floating rate payer. The fixerate is 4%, with annpayments. The notionpriciple is $5,000,000. The spot interest rates are follows: one year, 3.5%; two years, 4.5%. Toy is the reset y, the current value of the sw is closest to:A.$54,437.B.$-54,437.C.-$30,125.$30,125. B is correct.考点利率互换估值.解析支浮动的一方可以看作一个浮动利率债券，浮动利率债券在reset y 价值回归面值。收固定的一方可以看作一个固定利率债券，Bfix =0.04e−0.035+1.04e−0.045×2=0.989113B_{fix}\;=0.04e^{-0.035}+1.04e^{-0.045\times2}\\=0.989113Bfix=0.04e−0.035+1.04e−0.045×2=0.989113lV=(0.989113−1)×5,000,000=−54,437{l}\\V=(0.989113-1)\times5,000,000=-54,437lV=(0.989113−1)×5,000,000=−54,437 老师，题目里的“Toy is the reset y”是什么意思啊？
NO.PZ2019052801000049 问题如下 A bank entereinto a swwith two years to maturity a floating rate payer. The fixerate is 4%, with annpayments. The notionpriciple is $5,000,000. The spot interest rates are follows: one year, 3.5%; two years, 4.5%. Toy is the reset y, the current value of the sw is closest to: A.$54,437. B.$-54,437. C.-$30,125. $30,125. B is correct.考点利率互换估值.解析支浮动的一方可以看作一个浮动利率债券，浮动利率债券在reset y 价值回归面值。收固定的一方可以看作一个固定利率债券，Bfix =0.04e−0.035+1.04e−0.045×2=0.989113B_{fix}\;=0.04e^{-0.035}+1.04e^{-0.045\times2}\\=0.989113Bfix=0.04e−0.035+1.04e−0.045×2=0.989113lV=(0.989113−1)×5,000,000=−54,437{l}\\V=(0.989113-1)\times5,000,000=-54,437lV=(0.989113−1)×5,000,000=−54,437 如题
NO.PZ2019052801000049问题如下A bank entereinto a swwith two years to maturity a floating rate payer. The fixerate is 4%, with annpayments. The notionpriciple is $5,000,000. The spot interest rates are follows: one year, 3.5%; two years, 4.5%. Toy is the reset y, the current value of the sw is closest to:A.$54,437.B.$-54,437.C.-$30,125.$30,125. B is correct.考点利率互换估值.解析支浮动的一方可以看作一个浮动利率债券，浮动利率债券在reset y 价值回归面值。收固定的一方可以看作一个固定利率债券，Bfix =0.04e−0.035+1.04e−0.045×2=0.989113B_{fix}\;=0.04e^{-0.035}+1.04e^{-0.045\times2}\\=0.989113Bfix=0.04e−0.035+1.04e−0.045×2=0.989113lV=(0.989113−1)×5,000,000=−54,437{l}\\V=(0.989113-1)\times5,000,000=-54,437lV=(0.989113−1)×5,000,000=−54,437 题目中说浮动用的是payer，固定用的是payment，那到底哪个是付出，哪个是收到怎么区分？
