问题如下：
A bond portfolio manager wants to reduce the duration from 5.5 to 4.5 by 3-year interest rate swap with quarterly payments, the market value of portfolio is $10,000,000. The modified duration of the fixed-rate bond is 2.25. The notional principle of swap is closest to:
选项：
A. $4,931,864
B. $4,705,882
C. $3,515,235
解释：
B is correct.
考点：用interest rate swap 改变duration
解析：
此题需要降低duration，因此应该进入payer swap，它的duration=浮动端duration-固定端duration
固定端的duration=2.25
浮动端的duration=1/2*1/4=0.125
Payer swap的duration=0.125-2.25=-2.125
NP=(4.5-5.5)*10,000,000/(-2.125)=$4,705,882
您好请问这个浮动端的duration 是怎么算出来的？基础班讲义142页的例题为什么不用算这一步啊？谢谢您