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Pavel Korchagin · 2024年01月30日

为什么我算的折现因子和题目不太一样?

NO.PZ2023020101000017

问题如下:

Whitney meets with Grand Manufacturing. This client is based in Hong Kong but requires a €25,000,000 one-year bridge loan to fund operations in Germany. Grand Manufacturing is currently able to borrow euros at an interest rate of 3.75% but wonders if there is a less expensive alternative. Whitney advises Grand to borrow in HK$ and enter into a one-year foreign currency swap with quarterly payments to receive euros at a fixed rate and pay HK$ at a fixed rate. The current exchange rate is HK$11.42 per €1, and the notional amounts will be exchanged at initiation and at maturity.

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.

Based on the information in Exhibit 1 and using a 30/360 day count, the annualized fixed rates on the currency swap suggested by Whitney for Grand for euros and Hong Kong dollars, respectively, will be closest to:

选项:

A.

2.34% and 1.87%.

B.

2.13% and 1.58%.

C.

2.32% and 1.85%.

解释:

C is correct. The appropriate PV factors for Euribor and Hibor are calculated from Exhibit 1.

rFIX,\euro=1.0PV0,tn(1)i=1nPV0,tn(1)=10.977135(3.945545)=0.005795r_{FIX,\backslash\mathrm{euro}}=\frac{1.0-PV_{0,t_n}(1)}{\sum_{i=1}^nPV_{0,t_n}(1)}=\frac{1-0.977135}{(3.945545)}=0.005795

rFIX,HK$=1.0PV0,tn(1)i=1nPV0,tn(1)=10.981643(3.958421)=0.004637r_{FIX,HK\$}=\frac{1.0-PV_{0,t_n}(1)}{\sum_{i=1}^nPV_{0,t_n}(1)}=\frac{1-0.981643}{(3.958421)}=0.004637

The annualized rate is simply (360/90) times the 90-day rates or 2.3181% for Euros and 1.8550% for HK$.


我算的B90=1/(1+1.86%)^0.25=0.995403

1 个答案

pzqa35 · 2024年01月30日

嗨,努力学习的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。因此折现因子也是使用单利来进行计算的哈。B90=1/(1+1.86%*0.25)=0.995372.

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