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king · 2024年04月13日

这道题目什么时候会用到期初的汇率呢?

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 bridgeloan to fund operations in Germany. Grand Manufacturing is currently able toborrow euros at an interest rate of 3.75% but wonders if there is a lessexpensive alternative. Whitney advises Grand to borrow in HK$ and enter into aone-year foreign currency swap with quarterly payments to receive euros at afixed rate and pay HK$ at a fixed rate. The current exchange rate is HK$11.42per €1, and the notional amounts will be exchanged at initiation and atmaturity.

Exhibit1 Current Term Structure of Rates (%)

Note: Libor is theLondon 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 theinformation in Exhibit 1 and using a 30/360 day count, the annualized fixedrates on the currency swap suggested by Whitney for Grand for euros and HongKong 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 factorsfor 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$.


如果都是分别根据各自的折现因子来计算swap rate 的话,期初利率是否只是在计算value的时候有用呢?

1 个答案

李坏_品职助教 · 2024年04月14日

嗨,从没放弃的小努力你好:


计算value一般是在期初之后的某个t时刻,可以参考这道题后面那道题。

比如在t=90天的时候对这个swap计算value,用的是t时刻的汇率9.96进行货币单位转换.


而0时刻的汇率决定的是currency swap签订期间,两种货币的本金。比如这个题目里,期初汇率是11.42,那么就决定了HKD(港币本金)是285,500,000,EUR(欧元本金)是25,000,000,因为HKD 285500000 = EUR25000000 * 11.42


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