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薛真 · 2020年03月16日

问一道题：NO.PZ2020021204000037

  1. FRM I
  2. Financial Markets And Products

问题如下：

The Eurodollar futures price for a contract that matures in three years is 95.75. The standard deviation of the change in the short rate in one year is 0.8%. Estimate the continuously compounded forward rate between three and 3.25 years.

选项：

解释：

The actual/360 futures rate is 100 - 95.75 = 4.25. This is 4.25 X 365/360 = 4.3090% on an actual/actual basis.

This rate is compounded quarterly. The rate with continuous compounding is 4 X ln(1 + 0.043090/4) = 0.042860

or 4.2860%. The convexity adjustment is 0.5 X 0.0082 X 3 X 3.25 = 0.000312

An estimate of the continuously compounded forward rate is therefore:

0.042860 - 0.000312 = 0.042548 or 4.255%.

为什么利率用（1+r/4）不用（1+R）^0.25，谢谢老师

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1 个答案

小刘_品职助教 · 2020年03月16日

同学你好，

这道题是这样的，先将A/360转化为A/A，然后再转化为连续复利。

计算出来A/A利率是4.3090% ，按季复利，所以是（1+0.043090/4)=e^(r*0.25)

计算出r就是复利形式，等式两边同时取对数r=4*ln（1+0.043090/4)

不用（1+R）^0.25是因为A/A不是连续复利

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2024-11-08 17:01 1 · 回答

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