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jacqie · 2022年02月27日

这个转换公式是怎么得到的？

  1. FRM I
  2. Financial Markets And Products

NO.PZ2020021204000037

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%.

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

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1 个答案

品职答疑小助手雍 · 2022年02月28日

同学你好，假设连续复利的年化利率是r，现在季度复利的结果是4.309%，那么e^r=(1+4.309%/4)^4，解r即可。

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NO.PZ2020021204000037 问题如下 The Eurollfutures prifor a contrathmatures in three years is 95.75. The stanrviation of the change in the short rate in one yeis 0.8%. Estimate the continuously compounforwarrate between three an3.25 years. The actual/360 futures rate is 100 - 95.75 = 4.25. This is 4.25 X 365/360 = 4.3090% on actual/actubasis.This rate is compounquarterly. The rate with continuous compounng is 4 X ln(1 + 0.043090/4) = 0.042860or 4.2860%. The convexity austment is 0.5 X 0.0082 X 3 X 3.25 = 0.000312estimate of the continuously compounforwarrate is therefore:0.042860 - 0.000312 = 0.042548 or 4.255%. 不明白，请讲解一下这道题的解题思路和步骤

2024-11-08 17:01 1 · 回答

NO.PZ2020021204000037 问题如下 The Eurollfutures prifor a contrathmatures in three years is 95.75. The stanrviation of the change in the short rate in one yeis 0.8%. Estimate the continuously compounforwarrate between three an3.25 years. The actual/360 futures rate is 100 - 95.75 = 4.25. This is 4.25 X 365/360 = 4.3090% on actual/actubasis.This rate is compounquarterly. The rate with continuous compounng is 4 X ln(1 + 0.043090/4) = 0.042860or 4.2860%. The convexity austment is 0.5 X 0.0082 X 3 X 3.25 = 0.000312estimate of the continuously compounforwarrate is therefore:0.042860 - 0.000312 = 0.042548 or 4.255%. 基础课讲义里面并没有提到futrues利率转成forwar时候需要按天数调整，只给了减去方差的调整项，考试里面也要这样按actual转化吗？还是可以直接用futures的利率减去调整项就可以？

2024-10-19 17:15 1 · 回答

NO.PZ2020021204000037问题如下The Eurollfutures prifor a contrathmatures in three years is 95.75. The stanrviation of the change in the short rate in one yeis 0.8%. Estimate the continuously compounforwarrate between three an3.25 years.The actual/360 futures rate is 100 - 95.75 = 4.25. This is 4.25 X 365/360 = 4.3090% on actual/actubasis.This rate is compounquarterly. The rate with continuous compounng is 4 X ln(1 + 0.043090/4) = 0.042860or 4.2860%. The convexity austment is 0.5 X 0.0082 X 3 X 3.25 = 0.000312estimate of the continuously compounforwarrate is therefore:0.042860 - 0.000312 = 0.042548 or 4.255%. 4.25*365/360=4.3090％4.3090%/4=1.0773％e^1.0773％*4 是这样么？

2024-03-31 21:22 1 · 回答

NO.PZ2020021204000037问题如下 The Eurollfutures prifor a contrathmatures in three years is 95.75. The stanrviation of the change in the short rate in one yeis 0.8%. Estimate the continuously compounforwarrate between three an3.25 years.The actual/360 futures rate is 100 - 95.75 = 4.25. This is 4.25 X 365/360 = 4.3090% on actual/actubasis.This rate is compounquarterly. The rate with continuous compounng is 4 X ln(1 + 0.043090/4) = 0.042860or 4.2860%. The convexity austment is 0.5 X 0.0082 X 3 X 3.25 = 0.000312estimate of the continuously compounforwarrate is therefore:0.042860 - 0.000312 = 0.042548 or 4.255%. ​两步计算没看懂

2024-03-31 14:58 1 · 回答

NO.PZ2020021204000037 问题如下 The Eurollfutures prifor a contrathmatures in three years is 95.75. The stanrviation of the change in the short rate in one yeis 0.8%. Estimate the continuously compounforwarrate between three an3.25 years. The actual/360 futures rate is 100 - 95.75 = 4.25. This is 4.25 X 365/360 = 4.3090% on actual/actubasis.This rate is compounquarterly. The rate with continuous compounng is 4 X ln(1 + 0.043090/4) = 0.042860or 4.2860%. The convexity austment is 0.5 X 0.0082 X 3 X 3.25 = 0.000312estimate of the continuously compounforwarrate is therefore:0.042860 - 0.000312 = 0.042548 or 4.255%. 最后的一句的问题是说计算连续复利的forwarrate，对吗？Efutures 报价100-R，R是单利，对吗？为什么要计算futures rate连续复利，Efutures 都是连续复利的吗？还是forwarrate 没法计算连续复利？我说清楚了吗，请老师帮解答，谢谢。

2024-03-22 21:24 1 · 回答