NO.PZ2021120102000004
问题如下：
An investment manager is considering decreasing portfolio duration versus a benchmark index given her expectations of an upward parallel shift in the yield curve.
If she has a choice between a callable, putable, or option-free bond with otherwise comparable characteristics, the most profitable position would be to:
选项：
A. own
the callable bond.
own the putable bond.
own the option-free bond.
解释：
B is correct. The value of a bond with an embedded option is equal to the sum of the value of an option-free bond plus the value to the embedded option.
With a putable bond, the embedded put option is
owned by the bond investor, who can exercise the
option if yields-to-maturity increase, as in this scenario.
Under A, the embedded call option is owned by
the bond issuer, who is more likely to exercise if
yields-to-maturity decrease (that is, the bond investor is short the call
option).
As for C, the option-free bond underperforms the putable bond given the rise in value of the embedded put option.
老师，我的理解是（如有误请指正）：
Vcallable bond = Voption-free-bond - Voption
Vputable bond = Voption-free-bond + Voption
当r上升，putable bond更可能执行所以Voption增加，但是同时Voption-free-bond本身价格会降低所以Value变小，所以对Vputable bond是一增一减的效果， 相互抵消；
当r上升，callable bond不太可能执行所以Voption减少，也就是减掉了一个更小的数字，会增加Vcallable bond, 但是同时Voption-free-bond本身价格会降低所以Value变小，相互抵消；
两种情况都是相互抵消，怎么知道哪个更好呢？是不是因为题目说了要short duration而putable bond会执行duration更小,所以才选的？
