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Flying马 · 2024年03月06日

计算器步骤

  1. CFA I
  2. Quantitative

NO.PZ2023052407000011

问题如下：

The current exchange rate between the euro and US dollar is USD/EUR1.025. Risk-free interest rates for one year are 0.75 percent for the euro and 3.25 percent for the US dollar. The one-year USD/EUR forward rate that best prevents arbitrage opportunities is:

选项：

A.

USD/EUR1.051

B.

USD/EUR1.025

C.

USD/EUR0.975

解释：

A is correct. To avoid arbitrage opportunities in exchanging euros and US dollars, investors must be able to lock in a one-year forward exchange rate of USD/EUR1.051 today. The solution methodology is shown below.

In one year, a single unit of euro invested risk-free is worth EUR1.0075 (=e0.0075).

In one year, a single unit of euro converted to US dollars and then invested risk-free is worth USD1.0589 (=1.025*e0.0325).

To convert USD1.0589 into EUR1.0075 requires a forward exchange rate of USD/EUR1.051 (=1.0589/1.0075).

请问这道题怎么按呢。

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品职助教_七七 · 2024年03月06日

嗨，努力学习的PZer你好：


根据此处基础班讲解的便捷公式，F=S0×e^(rUSD-rEUR)，代入题干数字后得到

F=1.025×e^(3.25%-0.75%)

首先计算0.0325-0.0075=0.025，然后在此基础上按2nd+LN，得到e^(3.25%-0.75%)=1.0253.

此后正常乘以1.025，得到答案1.0509，选择A选项。

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