问题如下图：
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解释：
老师，请问既然是call at par,为什么不是100.8789-100呢？谢谢
吴昊_品职助教 · 2019年04月28日
我们现在要求的是callable bond中的embedded option价值，value of call option=value of straight bond-value of callable bond。不含权债券的value是100.8789，但是callable bond的价值不是面值。在求callable bond value的时候，需要我们从后往前折现，并且比较每一个时间点的折现值和面值的大小。call at par的意思是一旦折现值触发了行权价，我们要将折现值调整回面值。callable bond在利率下降的时候，债券发行人会提前赎回债券，所以涨幅有限，价格有一个上限，即call price。所以一旦折现值大于了100，我们要将折现值调整回100，这就是call at par的意思，并不代表callable bond value就是100.
NO.PZ2018123101000086 问题如下 Exhibit 1 shows par, spot, anone-yeforwarrates.Bon4 is a fixeRate Bon of Alpha Corporation, with 1.55% annucoupon ancallable pwithout any lockout perio. The bonmaturity is 3 years.Baseon the information above, the value of the embeeoption in Bon4 is closest to: A.nil. B.0.1906. C.0.8789. C is correct.考点考察对含权债券的理解解析债券4是可Callable。其价值为Value of callable bon= value of straight bon– value of call option on bon此，Embeecall option的价值为Value of call option on bon= Value of straight bon– Value of callable bon用Spot rate对该Straight bon行定价为1.55(1.0100)1+1.55(1.012012)2+101.55(1.012515)3=100.8789\frac{1.55}{{(1.0100)}^1}+\frac{1.55}{{(1.012012)}^2}+\frac{101.55}{{(1.012515)}^3}=100.8789(1.0100)11.55+(1.012012)21.55+(1.012515)3101.55=100.8789无赎回保护期的可赎回债券的价值不能超过100，因此call option的价值为=100.8789–100=0.8789。 解析里Call option的Value是100.8789-100=0.8789，但是提问中回答是100.8789-100.5446=0.3343，哪种算法才是正确的呢？
NO.PZ2018123101000086 问题如下 Exhibit 1 shows par, spot, anone-yeforwarrates.Bon4 is a fixeRate Bon of Alpha Corporation, with 1.55% annucoupon ancallable pwithout any lockout perio. The bonmaturity is 3 years.Baseon the information above, the value of the embeeoption in Bon4 is closest to: A.nil. B.0.1906. C.0.3343. C is correct.考点考察对含权债券的理解解析债券4是可Callable。其价值为Value of callable bon= value of straight bon– value of call option on bon此，Embeecall option的价值为Value of call option on bon= Value of straight bon– Value of callable bon用Spot rate对该Straight bon行定价为1.55(1.0100)1+1.55(1.012012)2+101.55(1.012515)3=100.8789\frac{1.55}{{(1.0100)}^1}+\frac{1.55}{{(1.012012)}^2}+\frac{101.55}{{(1.012515)}^3}=100.8789(1.0100)11.55+(1.012012)21.55+(1.012515)3101.55=100.8789而Callable bon定价需要使用1-yeforwarrate，将债券的现金流从最后一期开始，依次向前一个节点折现，以判断折现值是否会触发行权价；使用表格中的Forwarrate对Callable bon行定价因此Call option的Value为100.8789-100.5446=0.3343 相同的题目编号，NO.PZ201712110200000304这道题的题解The value of a callable bon(par) with no call protection periocannot excee100, thprior higher the bonwoulcallet=0时刻也能call
NO.PZ2018123101000086 问题如下 Exhibit 1 shows par, spot, anone-yeforwarrates.Bon4 is a fixeRate Bon of Alpha Corporation, with 1.55% annucoupon ancallable pwithout any lockout perio. The bonmaturity is 3 years.Baseon the information above, the value of the embeeoption in Bon4 is closest to: A.nil. B.0.1906. C.0.3343. C is correct.考点考察对含权债券的理解解析债券4是可Callable。其价值为Value of callable bon= value of straight bon– value of call option on bon此，Embeecall option的价值为Value of call option on bon= Value of straight bon– Value of callable bon用Spot rate对该Straight bon行定价为1.55(1.0100)1+1.55(1.012012)2+101.55(1.012515)3=100.8789\frac{1.55}{{(1.0100)}^1}+\frac{1.55}{{(1.012012)}^2}+\frac{101.55}{{(1.012515)}^3}=100.8789(1.0100)11.55+(1.012012)21.55+(1.012515)3101.55=100.8789而Callable bon定价需要使用1-yeforwarrate，将债券的现金流从最后一期开始，依次向前一个节点折现，以判断折现值是否会触发行权价；使用表格中的Forwarrate对Callable bon行定价因此Call option的Value为100.8789-100.5446=0.3343 老师，二叉树求债券时，二叉树的利率都是forwarrate对吗？
NO.PZ2018123101000086 问题如下 Exhibit 1 shows par, spot, anone-yeforwarrates.Bon4 is a fixeRate Bon of Alpha Corporation, with 1.55% annucoupon ancallable pwithout any lockout perio. The bonmaturity is 3 years.Baseon the information above, the value of the embeeoption in Bon4 is closest to: A.nil. B.0.1906. C.0.3343. C is correct.考点考察对含权债券的理解解析债券4是可Callable。其价值为Value of callable bon= value of straight bon– value of call option on bon此，Embeecall option的价值为Value of call option on bon= Value of straight bon– Value of callable bon用Spot rate对该Straight bon行定价为1.55(1.0100)1+1.55(1.012012)2+101.55(1.012515)3=100.8789\frac{1.55}{{(1.0100)}^1}+\frac{1.55}{{(1.012012)}^2}+\frac{101.55}{{(1.012515)}^3}=100.8789(1.0100)11.55+(1.012012)21.55+(1.012515)3101.55=100.8789而Callable bon定价需要使用1-yeforwarrate，将债券的现金流从最后一期开始，依次向前一个节点折现，以判断折现值是否会触发行权价；使用表格中的Forwarrate对Callable bon行定价因此Call option的Value为100.8789-100.5446=0.3343 用forwarrate给含权债券估值是考纲内容吗？对应基础班讲义哪个位置？
NO.PZ2018123101000086 问题如下 Exhibit 1 shows par, spot, anone-yeforwarrates.Bon4 is a fixeRate Bon of Alpha Corporation, with 1.55% annucoupon ancallable pwithout any lockout perio. The bonmaturity is 3 years.Baseon the information above, the value of the embeeoption in Bon4 is closest to: A.nil. B.0.1906. C.0.3343. C is correct.考点考察对含权债券的理解解析债券4是可Callable。其价值为Value of callable bon= value of straight bon– value of call option on bon此，Embeecall option的价值为Value of call option on bon= Value of straight bon– Value of callable bon用Spot rate对该Straight bon行定价为1.55(1.0100)1+1.55(1.012012)2+101.55(1.012515)3=100.8789\frac{1.55}{{(1.0100)}^1}+\frac{1.55}{{(1.012012)}^2}+\frac{101.55}{{(1.012515)}^3}=100.8789(1.0100)11.55+(1.012012)21.55+(1.012515)3101.55=100.8789而Callable bon定价需要使用1-yeforwarrate，将债券的现金流从最后一期开始，依次向前一个节点折现，以判断折现值是否会触发行权价；使用表格中的Forwarrate对Callable bon行定价因此Call option的Value为100.8789-100.5446=0.3343 这什么原理？不用二叉树也能求含权bon格了吗？怎么没印象课上讲过？