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暖暖 · 2025年02月09日

可以用画图法做一遍这道题吗？看不懂公式。

  1. CFA II
  2. Derivative

NO.PZ2023020101000018

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 a fixedrate and pay HK$ at a fixed rate. The current exchange rate is HK$11.42 per €1,and the notional amounts will be exchanged at initiation and at maturity.The annualized rate is 2.3181% for Euros and 1.8550% for HK$.

Ninety days have passed since Whitney’sinitial meetings, and in the interim interest rates have increased dramatically.Whitney’s clients have asked to meet with her to review their positions.

In order to prepare for the meeting,Whitney has obtained updated interest rate data that is presented in Exhibit 2.In addition, she determines that the exchange rate for the Hong Kong dollar isHK$9.96 per €1, and the US stock index is at 905Exhibit 2: Present Value FactorsBased on Current Australian Term Structure.

Exhibit 2Term Structure of Rates 90 Days Later (%)

Note: Euribor isEuro Interbank Offered Rate. Hibor is the Hong Kong Interbank Offered Rate. Allrates shown are annualized

Using the data in Exhibit 2, the market value of GrandManufacturing’s swap after 90 days is closest to:

选项：

A.

–€4,103,142

B.

€2,701,178

C.

€3,625,900

解释：

Grand borrows HK$285,500,000 and exchangesit for €25,000,000 based on the initial exchange rate of HK$11.42 per euro.

Grand will pay an interest rate of 1.8550%on the borrowed HK dollars and earn 2.3181% on the lent/invested euros.

Ninety days into the swap, the exchangerate is HK$9.96, and the PV factors are:

Va=NAa,0(rFIX,a,0∑i=1nPVt,ti,a+PVt,tn,a)−S0NAb,0(rFIX,b,0∑i=1nPVt,ti,b+PVt,tn,b)V_a=NA_{a,0}(r_{FIX,a,0}\sum_{i=1}^nPV_{t,t_i,a}+PV_{t,t_n,a})-S_0NA_{b,0}(r_{FIX,b,0}\sum_{i=1}^nPV_{t,t_i,b}+PV_{t,t_n,b})€

=285,500,000/HK$/€9.96×[0.004637(2.9632)+0.980152]-€25,000,000×[0.005795(2.9552)+0.977422] =€28,489,585-€24,863,685=€3,625,900

我自己计算了每期的固定利息，欧元是0.144881M， 港币是1.324M。然后把每期的固定利息和期末的本金往90天处折现。然后向上箭头-向下剪头。算出来不对。谢谢

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1 个答案

李坏_品职助教 · 2025年02月09日

嗨，从没放弃的小努力你好：


本题的公司的意图是为了借到欧元融资，但是他现在希望通过swap来完成欧元融资，也就是公司希望在currency swap里面进行如下的交换：期初收取欧元、支付港币，期间收取港币利息、支付欧元利息，期末收取港币本金、支付欧元本金。并且是“quarterly payments”，也就是90天支付一次利息。

现在是在第90天，问你这个currency swap的价值是多少？

由于现在就是90天的时刻，所以第一笔利息不用考虑了，我们只需要考虑之后的180天、270天和360天的现金流。


1.先看支付的欧元现金流：未来支付的欧元现金流 = 180天的利息 + 270天的利息 + 360天的利息和本金，每一次支付的欧元利息=欧元本金25000000 * 欧元利率2.3181% / 4 = 144881欧元。而最后的欧元本金NP = 25000000欧元。

欧元的现金流折现之和 = 144881 * （1/（1+2.94%*90/360） + 1/(1+3.03%*180/360) + 1/(1+3.08% * 270/360)）+ 25000000 * 1/(1+3.08% * 270/360) ≈ 24863685欧元


2.再来看收取的港币现金流：未来收取的港币 = 180天的利息 + 270天的利息 + 360天的利息和本金，每一次利息=285,500,000 港币 * 1.855% / 4 = 1324006港币。而最后的本金NP = 285500000港币。

计算收取的这些港币的现值之和：

港币的现金流折现之和 = 1324006 * （1/（1+1.95%*90/360） + 1/(1+2.45%*180/360) + 1/(1+2.7% * 270/360)）+ 285500000* 1/(1+2.7% * 270/360) =283756689港币，用这个港币金额除以90天时刻的汇率9.96得到等值的欧元金额：28489627欧元。


最后用收取的港币现值之和28489627欧元 - 支付的欧元现值之和24863685欧元，得到最终结果3625942欧元。也就是C选项。

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