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关于计算Coupon的swap利率换算问题

NO.PZ2023020101000014

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：

–$602,250.

–$2,875,000.

–$2,408,880.

解释：

The present value factors for Exhibit 2 are provided below:

For example, PV(180) is calculated as:

$\frac1{1+0.0262\times(180/360)}=0.987069$

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:

$FB=C\sum_{i=1}^nPV_{t,ti}(1)+PV_{0,t_n}=0.008396(0.994505+0.987069+0.972786)+0.972786=0.997591$

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 × (0.997591 – 1.000) = –$602,250.

Using an alternative approach, the new fixed swap rate would be

$r_{FIX}=\frac{1.0-PV_{0,t_n}(1)}{\sum_{i=1}^nPV_{0,t_n}(1)}=1.0-0.972786/0.994505+0.987069+0.972786=0.009211$

And the value of the swap is the difference between the value at the old rate and the value at the new rate, or

$V=(FS_0-FS_t)\sum_{i=1}^nPV_{t,t_i}=(0.008396-0.009211)\times(0.9945+0.9871+0.9728)=-0.002409$

The swap value = $250,000,000 × –0.002409 = –$602,250

0.008396关于这个利率

提供给定的是1.6792%的swap利率，计算过程中我按照C/NP*(360/90) = 1.6792%来计算出的C=0.004198*NP

我发现这个0.008396是按照semi annual来计算C的，也就是C/NP*（360/180）=1.6792%，C = 0.008396*NP，而非按照题目中给定的quarter季度计算的。

我对这个数字很困惑，请麻烦老师解答一下。

关于计算Coupon的swap利率换算问题

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