问题如下图：
选项：
A. 
B. 
C. 
解释：
我找到了何老师讲的讲义相关部分，还有另外一个提问的同学的解答，还是不明白为什么flatten会是默认成曲线向下移动同时flatten，而不是曲线整体向上移动同时flatten（比如短期利率上升的多一些，远期利率上升的少一些）？
发亮_品职助教 · 2018年05月07日
也可以是你说的那种情况。
关于，利率曲线的flattening，关注的核心是：曲线更加平坦；即，短期利率和长期利率的Gap在减少。
如果没有具体描述短期利率或者长期利率之前的图形是什么样，或者没有描述短期利率与长期利率是怎么变动的，只说了flattening，那么只能判断，长期和短期的Gap是减少的。
对于一般而言，利率曲线是upward sloping的，（二级里也学了很多理论在解释为什么长期要更高），如果在这种情况下说flatting，意味着短期利率和长期利率的差距减少。
于是，由短期利率和长期利率求出来的implied forward rate会更小，
如上图所示，如果r3，和r2之间的差距在变小，那么算出来的f2,1也在变小。
在倒推求含权债券的价值时，我们用的就是每个节点上的one-year forward rate，如果forward rate在减少，说明折现出来的值容易更大，在每个节点上发生被赎回的可能性加大。
当然，长期利率下移，也是flattening的一种，只记这一种情况来分析callable bond的权利价值，也算是一种简便方法。
NO.PZ201602270200002008 问题如下 8. All else being equal, if the shape of the yielcurve changes from upwarsloping to flattening, the value of the option embeein Bon#2 will most likely: A.crease. B.remain unchange C.increase. C is correct.Bon#2 is a callable bon anthe value of the embeecall option increases the yielcurve flattens. When the yielcurve is upwarsloping, the one-perioforwarrates on the interest rate tree are high anopportunities for the issuer to call the bonare fewer. When the yielcurve flattens or inverts, many nos on the tree have lower forwarrates, whiincreases the opportunities to call an thus, the value of the embeecall option. 那为什么不是bon值下降，被call回去可能降低，所以call option value下降
NO.PZ201602270200002008问题如下 Samuel Sons is a fixeincome specialty firm thoffers aisory services to investment management companies. On 1 October 20X0, Steele Ferguson, a senior analyst Samuel, is reviewing three fixerate bon issuea locfirm, Pro Star, InThe three bon, whose characteristiare given in Exhibit 1, carry the highest cret rating. The one-year, two-year, anthree-yeprates are 2.250%, 2.750%, an3.100%, respectively. Baseon estimateinterest rate volatility of 10%, Ferguson constructs the binomiinterest rate tree shown in Exhibit 2.On 19 October 20X0, Ferguson analyzes the convertible bonissuePro Stgiven in Exhibit 3. Thy, the market prices of Pro Star’s convertible bonancommon stoare $1,060 an$37.50, respectively8. All else being equal, if the shape of the yielcurve changes from upwarsloping to flattening, the value of the option embeein Bon#2 will most likely:A.crease.B.remain unchangeC.increase.C is correct.Bon#2 is a callable bon anthe value of the embeecall option increases the yielcurve flattens. When the yielcurve is upwarsloping, the one-perioforwarrates on the interest rate tree are high anopportunities for the issuer to call the bonare fewer. When the yielcurve flattens or inverts, many nos on the tree have lower forwarrates, whiincreases the opportunities to call an thus, the value of the embeecall option. 按照期权定价公式，rf下降，c的价格应该下降，为什么这里是上升呢？
NO.PZ201602270200002008 remain unchange increase. C is correct. Bon#2 is a callable bon anthe value of the embeecall option increases the yielcurve flattens. When the yielcurve is upwarsloping, the one-perioforwarrates on the interest rate tree are high anopportunities for the issuer to call the bonare fewer. When the yielcurve flattens or inverts, many nos on the tree have lower forwarrates, whiincreases the opportunities to call an thus, the value of the embeecall option. 其他条件不变的话bon2已经是会在ye1是in the money会行权的状态，如果yielcurve flatten并不会增加行权的nos数，这样理解对么？那在这个前提下应该如何理解option value increase呢？
remain unchange increase. C is correct. Bon#2 is a callable bon anthe value of the embeecall option increases the yielcurve flattens. When the yielcurve is upwarsloping, the one-perioforwarrates on the interest rate tree are high anopportunities for the issuer to call the bonare fewer. When the yielcurve flattens or inverts, many nos on the tree have lower forwarrates, whiincreases the opportunities to call an thus, the value of the embeecall option. 我是这样考虑的yielcurve从原本的upwar为flatten说明短期利率上升长期利率下降，远期我们不看，只看近期，所以利率上升，Callable option value不变，请问错哪了？