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Kiki · 2024年05月08日

折现因子PV90

  1. CFA II
  2. Derivative

NO.PZ2023020101000012

问题如下：

Meredith Whitney is a senior consultant in the Swaps Advisory Group of DCM Capital, an independent advisory firm. Whitney will be preparing to meet with three clients who need advice on structuring and implementing a swap program to manage their interest rate exposures. She is assisted by a junior analyst from the fixed income group, Toni Yang.

For her meetings, Whitney plans to use the data presented in Exhibit 1 below.

Exhibit 1 Current Term Structure of Rates (%)

Note: Libor is the London Interbank Offered Rate. Euribor is the Euro Interbank Offered Rate. Hibor is the Hong Kong Interbank Offered Rate. All rates shown are annualized.

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. Whitney’s first task is to determine the appropriate swap rate.

Using data in Exhibit 1 and a 30/360 day count, the annualized fixed rate of the swap recommended by Whitney for Novatel is closest to：

选项：

A.

2.22%.

B.

3.36%.

C.

5.15%.

解释：

The appropriate present value factors are provided below:

For example, PV(90) is calculated as follows:

Other present value factors are calculated in a similar manner.

The fixed rate is calculated as follows:

rFIX=1.0−PV0,tn(1)∑i=1nPV0,tn(1)=1.0−0.9669310.996463+0.990884+0.984349+0.966931=0.008396r_{FIX}=\frac{1.0-PV_{0,t_n}(1)}{\sum_{i=1}^nPV_{0,t_n}(1)}=\frac{1.0-0.966931}{0.996463+0.990884+0.984349+0.966931}=0.008396

The annualized rate =0.008396×360/90=0.033584.

折现因子怎么跟我算的不一样，不应该是1/（1+1.42%）^90/360吗

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已采纳答案

pzqa35 · 2024年05月08日

嗨，爱思考的PZer你好：


在我们衍生中，基于过去的习惯的沿用，对于FRA和swap的定价和估值我们都是按照单利来进行计算的，关于这一点老师在基础课也做过特别的说明哈。

所以这里的折现因子我们需要用单利来计算，也就是：PV（90）=1/(1+1.42%*90/360)=0.996463

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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