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James · 2023年12月19日

没懂为啥要换成e来计算

  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).

为什么是e的0.0075次方？

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1 个答案

品职助教_七七 · 2023年12月20日

嗨，努力学习的PZer你好：


对于数量科目这章下的汇率问题，教材统一都用连续复利来进行计算，也就是1元钱一年之后的本息和为1×e的r次方。

故1欧元一年之后的本息和为1×e的0.0075次方。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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