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中二 · 2020年02月17日

问一道题:NO.PZ2016070202000031 [ FRM II ]

问题如下:

What is the effect on the value of a callable convertible bond of a decrease in interest rate volatility and stock price volatility?

选项:

A.

An increase in value due to both interest rate volatility and stock price volatility

B.

An increase and decrease in value, respectively

C.

A decrease and increase in value, respectively

D.

A decrease in value due to both

解释:

A decrease in stock price volatility decreases the value of the equity conversion option and thus the convertible bond price. A decrease in interest rate volatility decreases the value of the interest rate call option. Because the bond investor is short the interest rate option, this increases the value of the convertible.

我可以理解convertible bond=bound-call option on call+call option on stock这个等式,当利率波动性下降时,等式右边的两个call option的价格都下降没问题,但是发生变化的是option的价格,call option on stock下降就说明stock的volatility也下降是什么依据呢?那又为什么covertible bond的volatility上升呢?

1 个答案

品职答疑小助手雍 · 2020年02月18日

同学你好,convertible bond=bond(1)-call option on bond(2)+call option on stock(3)

利率波动性下降(不是利率下降)和(3)没关系,只和(2)有关,会使(2)的价值下降,但因为(2)前面是减号,所以导致等式右边的式子变大。

股票波动性上升会使(3)变大,从而导致等式右边的式子变大。


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