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上小学 · 2023年03月05日

short. call option 价格上涨也必须行权,因此39—42不是—3吗?38—39=1

NO.PZ2020021205000055

问题如下:

A stock price is currently 40.It is known that it will be 42 or 38 at the end of a month.The risk-free rate is 4% per annum with continuous compounding. there is a one-month call option with a strike price of 39,what position should be taken in the stock to hedge a short position in the option?

解释:

The position is long 0.75 of a share. This is because a portfolio of 0.75 shares and short one option is worth 28.5 for both outcomes.

我计算c1+。为负三 C1- is 1

1 个答案

DD仔_品职助教 · 2023年03月06日

嗨,从没放弃的小努力你好:


同学你好,

short call一方没有权利只有义务,long方行权,short方必须配合。并且在计算delta也就是long的股票数时,delta对于call option而言全部都是正数,所以加个上升到42,期权费依旧是42-39=3,不分long方或者short方,或者可以说全部站在long方的角度。delta=期权费变化/基础资产价格变化=(3-0)/(42-38)=0.75。因为原本头寸是short call,要用long stock来对冲,所以就是long0.75stock

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