NO.PZ2023040701000073
问题如下：
Hsu then selects the four bonds issued by RW, Inc. given in Exhibit 2. These bonds all have a maturity of three years and the same credit rating. Bonds #4 and #5 are identical to Bond #3, an option-free bond, except that they each include an embedded option.
In Exhibit 2, the bond whose effective duration will lengthen if interest rates rise is:
选项：
A.Bond #3
Bond #4
Bond #5
解释：
Correct Answer: B
Effective duration indicates the sensitivity of a bond’s price to a 100 bps parallel shift of the benchmark yield curve assuming no change in the bond’s credit spread. The effective duration of an option-free bond such as Bond #3 changes very little in response to interest rate movements. As interest rates rise, a call option moves out of the money, which increases the value of the callable bond and lengthens its effective duration. In contrast, as interest rates rise, a put option moves into the money, which limits the price depreciation of the putable bond and shortens its effective duration. Thus, the bond whose effective duration will lengthen if interest rates rise is the callable bond, i.e., Bond #4.
题目问当利率上升，哪个的effective duration会增加？答案选callable bond.
我的理解是：当利率上升，不含权债券option-free bond的duration是不受影响的。callable bond此情况下不会行权，相当于一个不含权债券的效果，也就是仅单边受影响one-side。
同理，当callable bond或putable bond没法发挥时，他们的duration和convexity都表现的和普通不含权债券一样，不受利率变化影响。
我的这个理解不对吗？答案竟然说callable bond的duration增加了？
请老师解答一下，感谢~
