问题如下：
Whitney’s first meeting is with Novatel, a
US based company that currently has an outstanding loan of $250,000,000 that
carries a 5.15% fixed interest rate. Novatel’s managers feel that the current interest
rate on the loan is high and they also believe that interest rates are poised
to decline. Whitney advises Novatel to enter into a one-year pay-floating Libor
receive-fixed interest rate swap with quarterly payments. The notional
principal on the swap will be $250,000,000，and the annualized swap rate is 0.016792. Whitney’s first task is to
determine the appropriate swap rate.Ninety days have passed since Whitney’s
initial meetings, and in the interim interest rates have increased
dramatically. Whitney’s clients have asked to meet with her to review their
positions.In order to prepare for the meeting,
Whitney has obtained updated interest rate data that is presented in Exhibit 2.Exhibit
2 Term Structure of Rates 90 Days Later (%)
Using data in Exhibit 2 and a 30/360 day
count, the market value of Novatel’s swap after 90 days is closest to:
选项：
A.
–$3,702,900.
B.
–$2,875,000.
C.
–$2,408,880.
解释：
The
present value factors for Exhibit 2 are provided below:
For example, PV(180) is calculated as:
1+0.0262×(180/360)1=0.987069
Other present value factors are calculated
in a similar manner.
Using the fixed rate initially determined
for the swap and the current PV factors, the current value of the fixed bond
is:
FB=C∑i=1nPVt,ti(1)+PV0,tn=0.004198(0.994505+0.987069+0.972786)+0.972786=0.9851884
The value of the floating rate bond at reset is 1. The market
value of the pay-floating, receive fixed rate swap is the value of the
fixed-rate bond less the value of the floating-rate bond, or $250,000,000 ×
(0.9851884 – 1.000) = –$3,702,900.
Using an alternative approach, the new
fixed swap rate would be
rFIX=∑i=1nPV0,tn(1)1.0−PV0,tn(1)=1.0−0.972786/0.994505+0.987069+0.972786=0.00921147
And the value of the swap is the
difference between the value at the old rate and the value at the new rate, or
V=(FS0−FSt)∑i=1nPVt,ti=(0.004198−0.00921147)×(0.9945+0.9871+0.9728)=−0.0148116
The swap value = $250,000,000 × –0.0148116 = –$3,702,900
为什么要把给的FS0除以4？不要简单的说给的是年利率，按季度所以除4，按答案推这么简单的字面我能看不懂吗，为什么有的题FS0就不作处理直接用？为什么这道题就得除4？题目给的条件有什么差异？根源是在哪儿？我要听这个。而且为什么不把FSt年化，乘以4，直接用给的FS0去减乘4的FSt？
