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BillZ · 2025年02月01日

interest rate volatility

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NO.PZ202209060200004406

问题如下:

Based on Choate’s final comments and the COF portfolio positions in Exhibit 1, Choate is most likely expecting:

选项:

A.improved real estate markets and higher interest rate volatility. B.lower interest rate volatility and increasing default correlations. C.lower interest rate volatility and decreasing default correlations.

解释:

Solution

B is correct. Choate expresses his belief that market expectations of interest rate volatility will decrease, so he buys agency MBS in the COF portfolio. The correlation of expected defaults on the collateral of a CDO affects the relative value between the senior and subordinated tranches; as default correlations increase, the value of mezzanine tranches usually increases relative to the value of senior tranches. Because he expects the correlation to be highly positive, he can try to profit by selling the lower yielding (or selling short) Class A and buying the higher yielding Class B.

A is incorrect because an investor buying MBS expects lower, not higher, volatility.

C is incorrect because an investor that expects higher correlations would short Class A and go long Class B.

老师,我看到有一个回答里说:long MBS=long option free bond+short volatility。我想请问下这个公式的含义,以及在讲义哪里有提到。

1 个答案

发亮_品职助教 · 2025年02月01日

原版书和讲义没有提到,这个是对债券特性的理解。把MBS当成callable bond分析。


MBS的底层资产是房贷。投资者买了MBS这种债券之后,也会定期收到coupon与本金现金流。这些现金流源自于:房贷的月供现金流。


当买房的人每月供月供时,这些现金流就会按照规则流入MBS投资者手中。

所以可以理解成,MBS的真正发行人是:买房贷款的人。

这些发行人(贷款人)每期归还贷款,也就是归还MBS投资者的coupon与本金现金流(通过房贷月供形式)


房贷一个特点就是,买房的人可以随时提前偿还房贷,这种提前偿还的现金流就会流向MBS的投资者,从MBS投资者手中提前把债券赎回回来。MBS投资者面临被提前赎回的风险。


这种赎回机制,就是callable bond。因为callable bond的发行人也是有权利提前将债券赎回。投资者也是面临被提前赎回的风险。


所以投资者买了MBS,可以当成投资callable bond。分析的原理一致。


long callable bond = long option-free bond + short call option

投资者买了callable bond后,相当于买了一个option-free bond,同时卖了一个call option给发行人。因为是发行人拥有权利,发行人是long call option,那么投资者就是short call option。


MBS也是同理,投资者买了MBS,头寸为:

long MBS = long option-free bond + short call option


是贷款买房子的人有权利提前偿还房贷,他们具有long call option,那么投资MBS的投资者,就是short call option。


而option,无论是call还是put,都是volatility的载体,只要long option,就是long volatiltiy。因为只有当volatility上升时,long option就有可能行权盈利。所以long option就是看多volatility,即long volatility。


short option就是认为波动率不会加大,不太可能会触发行权,所以才做short option的头寸,就是看空volatility,于是short option就是short volatility的头寸。


总之,option看成volatility的载体。long option获得long volatility;

short option获得short volatility


所以Long MBS/Long callable bond里面,投资者是short call option,所以相当于是short volatility。

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