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熊猫666 · 2024年03月15日

老师你好，请问计算float rate的时候为什么是单利形式呢？

* 问题详情，请查看题干

NO.PZ202108100100000203

问题如下：

Based on Exhibit 3, Johnson should determine that the annualized equilibrium fixed swap rate for Japanese yen is closest to:

选项：

A.

0.0624%.

B.

0.1375%.

C.

0.2496%.

解释：

C is correct.

The equilibrium swap fixed rate for yen is calculated as

$r_{JPY}=\frac{1-PV_{n,JPY}(1)}{\sum_{i=1}^4PV_{i,JPY}(1)}$

The yen present value factors are calculated as

$PV(1)_{i,JPY}=\frac1{1+R_{spot_{i,JPY}}({\displaystyle\frac{NAD_i}{NTD}})}$

where

90-day PV factor =1/[1+0.0005(90/360)] = 0.999875.

180-day PV factor =1/[1+0.0010(180/360)] = 0.999500.

270-day PV factor =1/[ 1+0.0015(270/360)] = 0.998876.

360-day PV factor =1/[ 1+0.0025(360/360)] = 0.997506.

Sum of present value factors = 3.995757.

Therefore, the yen periodic rate is calculated as

$r_{JPY}=\frac{1-PV_n(1)}{\sum_{i=1}^4PV_i(1)}=\frac{1-0.997506}{3.995757}=0.000624=0.0624\%$

The annualized rate is (360/90) times the periodic rate of 0.0624%, or 0.2496%.

中文解析：

本题考察的是货币互换求定价。货币换求定价和普通的利率互换求定价是一样的，都是根据公式： $r_{JPY}=\frac{1-PV_{n,JPY}(1)}{\sum_{i=1}^4PV_{i,JPY}(1)}$ 来计算即可。

需要注意的是根据此公式求得的fixed rate需要年化后才是我们要求的swap rate。这里要和第（1）小问作一下区分。

老师你好，请问计算float rate的时候为什么是单利形式呢？能总结下，什么情况单利，什么情况复利么？

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李坏_品职助教 · 2024年03月15日

嗨，努力学习的PZer你好：

这个要根据CFA教材的规定来区分。

总结如下：

在衍生品中，凡是期限短于1年，都用单利。
如果题目是大于1年的期限，题目会写出annual compounded（离散复利），或者continious compounded（连续复利，就是e的n次方)。
如果没说明用哪一种，也没有出现continious compounded，那就默认是annual compounded（离散复利）。

----------------------------------------------
就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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2024-10-25 11:36 1 · 回答

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