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coupon rate 是年化的概念吗？

NO.PZ2016031001000063

问题如下：

An investor considers the purchase of a 2-year bond with a 5% coupon rate, with interest paid annually. Assuming the sequence of spot rates shown below, the price of the bond is closest to:

选项：

101.93.

102.85.

105.81.

解释：

A is correct.

The bond price is closest to 101.93. The price is determined in the following manner:

$PV=\frac{PMT}{{(1+Z_1)}^1}+\frac{PMT+FV}{{(1+Z_2)}^2}$

where:

PV = present value, or the price of the bond

PMT = coupon payment per period

FV = future value paid at maturity, or the par value of the bond

Z₁= spot rate, or the zero-coupon yield, for Period 1

Z₂= spot rate, or the zero-coupon yield, for Period 2

$PV=\frac5{{(1+0.03)}^1}+\frac{5+100}{{(1+0.04)}^2}$

PV = 4.85 + 97.08 = 101.93

考点：Pricing Bonds with Spot Rates

解析：通过未来现金流折现求和，第一年的现金流(5)用S1折现，第二年的现金流(5+100)用S2折现，可得债券价格为101.93，故选项A正确。

题目中的coupon rate 是5%,按年付，说是两年期的bond，为什么每一期的coupon 不是5%除以2 呢？这个coupon rate 是年化的概念吗？

嗨，爱思考的PZer你好：

1、coupon rate=5%，这是年化的概念。（我们所有能表示出来的利率，都是年化的概念）

2、定位到题目中：An investor considers the purchase of a 2-year bond with a 5% coupon rate, with interest paid annually. 现在这个债券是一年付息一次的，所以每一期的coupon payment = 100×5% = 5，不需要除以2。

3、如果我们现在将题目条件做一下修改，with interest paid semi-annually，债券一年付息两次，那么一期的coupon payment = 100×5%/2 = 2.5，才需要除以2。with interest paid quarterly，债券一年付息四次，那么一期的coupon payment = 100×5%/4 = 1.25，需要除以4.

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coupon rate 是年化的概念吗？

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