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Archie · 2022年05月07日

不明白算啥

  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.

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%.

😭别的同学看起来都知道了一些了，但是我好像完全没思路，老师能告诉一下思路嘛

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1 个答案

李坏_品职助教 · 2022年05月07日

嗨，努力学习的PZer你好：


题目给了你eurodollar 期货合约的价格信息，告诉了你short rate的σ是0.8%，让你推算在第三年和第3.25年之间的远期利率（forward rate）。具体知识点是讲义的 convexity adjustment：

这里的T就是3，futures rate需要先把（100-95.75=4.25）这个利率转化为按照实际365天计息的利率（4.309%），然后再把这个4.309%除以4，再利用连续复利公式ln(1+1.309%/4) * 4还原为真实的连续复利年利率。 最后按照讲义里的红框公式求解即可。


同学可以听一下经典题Section 20的3.2题，和这个题差不多。

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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%. 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

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2024-03-22 21:24 1 · 回答

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2024-03-22 15:21 1 · 回答

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2024-03-22 15:03 1 · 回答