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karweillas · 2024年03月06日

算出折现因子后的计算部分可以详细解释一下吗?

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=1.0PV0,tn(1)i=1nPV0,tn(1)=1.00.9669310.996463+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.

如上

1 个答案

李坏_品职助教 · 2024年03月06日

嗨,努力学习的PZer你好:


利率互换的fixed rate计算公式:

这里的PV0,t(1)指的是到期日(最长期限)对应的折现因子,也就是PV(360)。所以fixed swap rate = (1-PV(360)) / (4个折现因子求和) = 0.008396。


这个数据是一个季度的利率,还要进行年化处理: 0.008396×360/90=0.033584.

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