可以讲解一下利率下降，为啥effective duration 会上升吗？知识点忘记了
选项：
A. 
B. 
C. 
解释：
吴昊_品职助教 · 2020年02月04日
嗨，从没放弃的小努力你好：
Bond 3是一个putable bond，在利率上升的时候，债券持有人可以将债券提前卖还给发行人，由于提前结束现金流，此时平均还款期短，effective duration会下降。当利率下降的时候，putable bond就更像是一个不含权债券，债券持有人不会执行权利。和利率上升比，此时的effective duration更长。这道题A选项其实是比较putable bond在利率上升和利率下降两种情况下，债券duration的大小。
-------------------------------就算太阳没有迎着我们而来，我们正在朝着它而去，加油！
NO.PZ2018123101000104 问题如下 Steele Ferguson, a senior analyst Samuel, is reviewing threefixerate bon issuea locfirm, Pro Star, Inc.A fall in interest rates woulmost likely result in: A.a crease in the effective ration of Bon#3. B.Bon#3 having more upsi potentithBon#2. C.a change in the effective convexity of Bon#3 frompositive to negative. A fall in interestrates results in a rise in bonvalues. For a callable bonsuBon#2,the upsi potentiis cappebecause the issuer is more likely to call thebon In contrast, the upsi potentifor a putable bonsuBon#3 isuncappe Thus, a fall in interest rates woulresult in a putable bonhavingmore upsi potentithotherwise inticcallable bon Note thA isincorrebecause the effective ration of a putable bonincreases, notcreases, with a fall in interest rates—the bonis less likely to put anhus behaves more like option-free bon C is also incorrebecause theeffective convexity of a putable bonis always positive. It is the effectiveconvexity of a callable bonthwill change from positive to negative ifinterest rates fall anthe call option is nethe money. 老师，请问C怎么理解
NO.PZ2018123101000104问题如下Steele Ferguson, a senior analyst Samuel, is reviewing threefixerate bon issuea locfirm, Pro Star, Inc.A fall in interest rates woulmost likely result in: A.a crease in the effective ration of Bon#3. B.Bon#3 having more upsi potentithBon#2. C.a change in the effective convexity of Bon#3 frompositive to negative.A fall in interestrates results in a rise in bonvalues. For a callable bonsuBon#2,the upsi potentiis cappebecause the issuer is more likely to call thebon In contrast, the upsi potentifor a putable bonsuBon#3 isuncappe Thus, a fall in interest rates woulresult in a putable bonhavingmore upsi potentithotherwise inticcallable bon Note thA isincorrebecause the effective ration of a putable bonincreases, notcreases, with a fall in interest rates—the bonis less likely to put anhus behaves more like option-free bon C is also incorrebecause theeffective convexity of a putable bonis always positive. It is the effectiveconvexity of a callable bonthwill change from positive to negative ifinterest rates fall anthe call option is nethe money. 这是二级的考点吗？一级学过忘记了…老师请再讲解一下久期、修正久期和有效久期的概念以及讲解一下为什么a是错的？
NO.PZ2018123101000104 问题如下 Steele Ferguson, a senior analyst Samuel, is reviewing threefixerate bon issuea locfirm, Pro Star, Inc.A fall in interest rates woulmost likely result in: A.a crease in the effective ration of Bon#3. B.Bon#3 having more upsi potentithBon#2. C.a change in the effective convexity of Bon#3 frompositive to negative. A fall in interestrates results in a rise in bonvalues. For a callable bonsuBon#2,the upsi potentiis cappebecause the issuer is more likely to call thebon In contrast, the upsi potentifor a putable bonsuBon#3 isuncappe Thus, a fall in interest rates woulresult in a putable bonhavingmore upsi potentithotherwise inticcallable bon Note thA isincorrebecause the effective ration of a putable bonincreases, notcreases, with a fall in interest rates—the bonis less likely to put anhus behaves more like option-free bon C is also incorrebecause theeffective convexity of a putable bonis always positive. It is the effectiveconvexity of a callable bonthwill change from positive to negative ifinterest rates fall anthe call option is nethe money. 老师您好，关于A为什么是错的？effective ration 不是很理解，有点忘记ration是怎么计算了？
NO.PZ2018123101000104问题如下Steele Ferguson, a senior analyst Samuel, is reviewing threefixerate bon issuea locfirm, Pro Star, Inc.A fall in interest rates woulmost likely result in: A.a crease in the effective ration of Bon#3. B.Bon#3 having more upsi potentithBon#2. C.a change in the effective convexity of Bon#3 frompositive to negative. A fall in interestrates results in a rise in bonvalues. For a callable bonsuBon#2,the upsi potentiis cappebecause the issuer is more likely to call thebon In contrast, the upsi potentifor a putable bonsuBon#3 isuncappe Thus, a fall in interest rates woulresult in a putable bonhavingmore upsi potentithotherwise inticcallable bon Note thA isincorrebecause the effective ration of a putable bonincreases, notcreases, with a fall in interest rates—the bonis less likely to put anhus behaves more like option-free bon C is also incorrebecause theeffective convexity of a putable bonis always positive. It is the effectiveconvexity of a callable bonthwill change from positive to negative ifinterest rates fall anthe call option is nethe money. 老师，这里B中的upsi potential应该是怎么理解？是upsi wn的意思吗？就是从positive的，变成negative的可能性吗？
NO.PZ2018123101000104 请问怎么理解当interest rate下降时，callable bonconvexity从正变成负？