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这类型题目是否建议优先使用画图法？

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：

–$3,702,900.

–$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:

$FB=C\sum_{i=1}^nPV_{t,ti}(1)+PV_{0,t_n}=0.004198(0.994505+0.987069+0.972786)+0.972786=0.9851884$

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

$r_{FIX}=\frac{1.0-PV_{0,t_n}(1)}{\sum_{i=1}^nPV_{0,t_n}(1)}=1.0-0.972786/0.994505+0.987069+0.972786=0.00921147$

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

$V=(FS_0-FS_t)\sum_{i=1}^nPV_{t,t_i}=(0.004198-0.00921147)\times(0.9945+0.9871+0.9728)=-0.0148116$

The swap value = $250,000,000 × –0.0148116 = –$3,702,900

不知道是否记错，重新定价法有局限性，貌似是只能用于求每个期限的value

嗨，从没放弃的小努力你好：

对。虽然这个题目给的是重新定价法的解法，但是swap的题目应该优先考虑画图法，而且画图法也确实更直观。

站在T=90的时刻，把未来收取的所有现金流作为向上箭头（包括最后的本金），未来支付的所有现金流作为向下箭头。

最后向上箭头的现值 - 向下箭头的现值即可得出value。

需要注意的是，在reset date（就是交换现金流的时刻），浮动利率部分的现金流现值恰好等于本金，而固定利率的现金流现值需要折现求出。

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这类型题目是否建议优先使用画图法？

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