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410140980 · 2023年07月11日

股票只有一阶导

NO.PZ2016071602000019

问题如下:

Identify the risk in a convertible arbitrage strategy that takes long positions in convertible bonds hedged with short positions in Treasuries and the underlying stock.

选项:

A.

Short implied volatility

B.

Long duration

C.

Long stock delta

D.

Positive gamma

解释:

D is correct. This position is hedged against interest rate risk, so b. is wrong. It is also hedged against directional movements in the stock, so c. is wrong. The position is long an option (the option to convert the bond into the stock) so is long implied volatility, so a. is wrong. Long options positions have positive gamma.

老师这道题当中long delta选项,是不是股票只包含了一阶导的delta。(隐约在CFA还是FRM课程中听到老师提过)期权是包含了一阶导二阶导的,所以如果要想完全做neutral的策略得先将期权的二阶导对冲掉,在利用股票去对冲一阶导。

所以这道题long 可转转在short 股票,已经把一阶导的变化给对冲了,所以不选C

1 个答案

pzqa27 · 2023年07月11日

嗨,从没放弃的小努力你好:


delta的定义是股价变化对衍生品价格的影响,所以股票对自己求导完后是常数1,1再求导就是0了,这个常数求阶导没有任何实际意义,所以股票是线性工具,而刚好对冲掉可转债种期权的线性部分,只剩非线性部分

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