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ZJZJ · 2024年07月15日

推导

NO.PZ2023020101000016

问题如下:

Mehta, who is based in Hong Kong SAR and requires a €25,000,000 one-year bridge loan to fund operations in Germany. He wants to fund this loan at a competitive rate. Riley advises Mehta to borrow in HK dollars and enter into a one-year foreign currency swap to swap into euros. The current exchange rate is HK$9.15 per euro. Exhibit 1 below provides Hong Kong and euro spot interest rates and present value factors.

Exhibit 1: Hong Kong and Euro Spot Interest Rates

Based on the information in Exhibit 1, the annual fixed swap rate Mehta would pay is closest to

选项:

A.

0.47%.

B.

0.92%.

C.

1.88%.

解释:

PV factors for Euro are provided along with an explanation of how they are calculated:

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

11+0.0037290360=0.9991\frac1{1+0.00372\ast\frac{90}{360}}=0.9991

Other present value factors are calculated in a similar manner.

The fixed rate is calculated as follows:

1.00.99530.9991+0.9979+0.9967+0.9953=0.001178\frac{1.0-0.9953}{0.9991+0.9979+0.9967+0.9953}=0.001178

The annualized rate = 0.001178 × 4 = 0.004712.

老师,你好,我是这样做的,不知道为什么不对:

事件发生:

T0: borrow 25mn *9.15 HKD for EURO25mn;

T1: return HKD: 25*9.15 *(1+0.0935%).


Cash flow:

1.我没有假设quarterly compounding,认为t=1是唯一现金流交换时间

2.因为通过swap得到欧元,所以支付欧元;被支付港币floating rate

at t1:

c = 25mn EURO * swap rate

float leg = 25mn * 9.15 * 0.935%

在t1时候,EUR/HKD Swap back。


那么c & float leg discount to t0应该价格相等:

25mn EURO * swap rate *0.9953 = 25mn * 9.15 * 0.935% * 0.9907

所以swap rate = 8.5%.....


请问问题是哪里,而且为什么是quarterly compounding?

1 个答案
已采纳答案

李坏_品职助教 · 2024年07月15日

嗨,努力学习的PZer你好:


这个题目确实没有告诉按季度复利的条件,是题目疏忽了。考试中不会出现这个问题。

不过为了以防万一,考试中如果判断复利的频率,最好根据题目给的表格条件来判断,隔90天给了一个新的Spot rate,只能假设是季度复利。


任何swap都不可能只有一次现金流交换。


此外,计算 fixed swap rate我建议还是按照教材(或讲义)中的公式,先计算每个期限的present value factor,再用(1=PV(360)) / (PV求和)得出fixed rate。


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

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