Susie · 2023年04月17日

这题没理解为什么是3去出，coupon不是6吗？没理解解题思路

1. CFA I
2. Fixed Income

NO.PZ2022061303000023

问题如下：

Using the following US Treasury spot rates, the arbitrage-free value of a two-year $100 par value Treasury bond with a 6% coupon rate is closest to:

选项：

A.$107.03. B.$105.65. C.$99.75.

解释：

B is correct. The value of the bond is

3/(1+0.0160/2)^1+3/(1+0.0220/2)^2+3/(1+0.0270/2)^3+103/(1+0.0310/2)^4=105.65$\frac{3}{{\left(1+0.0160/2\right)}^1}+\frac{3}{{\left(1+0.0220/2\right)}^2}+\frac{3}{{\left(1+0.0270/2\right)}^3}+\frac{103}{{\left(1+0.0310/2\right)}^4}=105.65$

A is incorrect because it treats the spot rates as forward rates.

C is incorrect because it does not divide the annual spot rates by two in the calculation.

考点：Pricing Bonds with Spot Rates

解析：通过未来现金流折现求和，可得债券价格为105.65。注意，由于债券半年付息一次，因此表格中的spot rate和coupon rate都需要去年化，前三期的coupon为3，第四期的coupon为103。