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CFA二级重要知识点:OAS、Z-spread和Normal spread区别联系

2014-03-31 12:41阅读:
spread 通常所说的利差,主要有以下几种分类:
1.Normal spread:is the simplest of the spread measures to use and to understand.It is simply an issue's YTM minus the YTM of a Treasure security of similar maturity.
即:普通spread=债券到期收益率-无风险债券到期收益率,
也就是风险观察中常说的利差spread,或者是信用利差。


2.Zero volatility spread (Z-spread): is the equal amount that we must add to each rate on the Treasure spot yield curve in order to make the present value of the risky bond's cash flow equal to its market price.
For a risky bond, the value obtained from discounting the expected cash flows at treasury spot rates will be too high because the treasure spot rate are lower than those appropriate for a risky bond. In order to value it correctly, we have to increase each of the treasure spot rates by some equal amount so that the present value of the risky bond's cash flows discounted at the increased spot rates equals the market value of the bond.
Z-spread 与normal sp
read的区别在于,计算债券现值贴现率时,normal spread是 采用的1+到期收益率,
而z-spread采用的是不同期限所对应的无风险债券收益率,不同时期,无风险利率也不一样。
当无风险收益率曲线是水平的时候,normal spread=z-spread,
当无风险收益率曲线是向上或者向下的时候,因为有多期时间贴现,所以 二者不一样。
可以说z-spread更加相对准确些,特别是有了无风险债券对于的收益率曲线具体数值时。
3.Option adjusted spread (OAS):measure is used when a bond has embeded options.
A callable bond, for example, must have a greater yield than an identical option-free bond, and a greater nominal spread or z-spread.
Loosely speaking, the option adjusted spread takes the option yield component out of the Z-spread measure; the option adjusted spread is the spread to the Treasure spot rate curve that the bond would have if it were option-free.
Z-spread- OAS=option cost in percent
OAS spread 是不考虑期权在内的spread, 一个含权债券的spread必定高于去掉含权的债券的spread,多出的就是期权的成本,或者理解为多出的就是含权支出所对应风险的回报。
对于一个含权债券,根据其市价计算出的spread是z-spread,含有了期权在内的spread,这个spread的价格肯定高(假定call)。同条件的债券,如果不含权,那么spread必然低,二者spread的价差就是期权成本。
计算OAS的目的是可以度量相关期权的成本。
因此,假定知道了OAS,那么就可以定价相关债券的价值。
比如可转债估值中,通常可以理解为纯债价值+期权价值,
其中,纯债价值的估值中,可以通过设定该OAS spread 进行估值。
期权价值的估值中,可以采用BS模型估值,最后得到该转债估值。

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