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fengsj · 2020年03月14日

问一道题:NO.PZ2018123101000086

问题如下:

Exhibit 1 shows par, spot, and one-year forward rates.

Bond 4 is a fixed-Rate Bonds of Alpha Corporation, with 1.55% annual coupon and callable at par without any lockout periods. The bond maturity is 3 years.

Based on the information above, the value of the embedded option in Bond 4 is closest to:

选项:

A.

nil.

B.

0.1906.

C.

0.3343.

解释:

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 bond = value of straight bond – value of call option on bond

因此,Embedded call option的价值为:

Value of call option on bond = Value of straight bond – Value of callable bond

利用Spot rate对该Straight bond进行定价为:

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

而Callable bond的定价需要使用1-year forward rate,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Forward rate对Callable bond进行定价:

因此Call option的Value为:100.8789-100.5446=0.3343

我的问题是:一般在二叉树求bond value时,需要使用volatility,在mid rare(forwand rate)求上涨利率或下降利率,本题中直接使用mid rare(forwand rate)求解,不是很明白这样的算法,请问是否可以帮助解答,谢谢

1 个答案
已采纳答案

吴昊_品职助教 · 2020年03月15日

这里用到的是forward rate进行折现。

one-year forward rate其实和二叉树的原理是一样的,二叉树里面的各个利率都是本节点到下一个节点的one-year forward rate,只不过二叉树里的这个forward rate存在不同的可能,分别给予权重然后进行加权平均。而我们这道题就是单一的情况,概率取到100%,也就是forward rate是一个确定的数值,不存在两种情况而已。其实本质原理是一样的。

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