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cherrin · 2022年06月28日

为什么discount rate要除以2

  1. CFA I
  2. Fixed Income

NO.PZ2016031001000055

问题如下：

A bond offers an annual coupon rate of 5%, with interest paid semiannually. The bond matures in seven years. At a market discount rate of 3%, the price of this bond per 100 of par value is closest to:

选项：

A.

106.60.

B.

112.54.

C.

143.90.

解释：

B is correct.

The bond price is closest to 112.54.The formula for calculating this bond price is:

PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT+FV(1+r)14PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}\text{+}\cdots\text{+}\frac{PMT+FV}{{(1+r)}^{14}}

PV=2.5(1+0.015)1+2.5(1+0.015)2+2.5(1+0.015)3+⋯+2.5+100(1+0.015)14PV=\frac{2.5}{{(1+0.015)}^1}+\frac{2.5}{{(1+0.015)}^2}+\frac{2.5}{{(1+0.015)}^3}\text{+}\cdots\text{+}\frac{2.5+100}{{(1+0.015)}^{14}}

PV = 2.46 + 2.43 + 2.39 + … + 2.06 + 83.21 = 112.54

考点：bond valuation

解析：债券半年付息一次，每一期的coupon为100×5%/2=2.5，通过未来现金流折现求和，可得债券价格为112.54。

也可利用计算器：N=7×2=14，I/Y=3/2=1.5，PMT=5/2=2.5，FV=100，求得PV= -112.54

故选项B正确。



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1 个答案

吴昊_品职助教 · 2022年06月28日

嗨，努力学习的PZer你好：


题干中： with interest paid semiannually，债券半年付息一次。因此所有的利率都是需要去年化的。

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努力的时光都是限量版，加油！

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2020-10-06 11:05 1 · 回答

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2020-09-02 22:54 1 · 回答

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2020-08-31 23:59 2 · 回答