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NO.PZ2023091802000142

问题如下：

Mr. Black has been asked by a client to write a large put option on the S&P 500 index. The option has an exercise price and a maturity that is not available for options traded on exchanges. He, therefore, has to hedge the position dynamically. Which of the following statements about the risk of his position are not correct?

选项：

He can make his portfolio delta neutral by shorting index futures contracts.

There is a short position in an S&P 500 futures contract that will make his portfolio insensitive to both small and large moves in the S&P 500.

A long position in a traded option on the S&P 500 will help hedge the volatility risk of the option he has written.

To make his hedged portfolio gamma neutral, he needs to take positions in options as well as futures.

解释：

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李坏_品职助教 · 2023年10月22日

嗨，从没放弃的小努力你好：

题目说这个人卖出了大量的SP500股票指数看跌期权。这个人必须要对这个仓位进行动态对冲。

做空了看跌期权，那么如果SP500大幅下跌，会使得他遭受亏损。所以需要做空股票（或者做空股票期货）来对冲看跌期权的空头风险，而且要不停的调整手里的股票数量）。

做空期货带来了负的delta，而看跌期权的空头自带正的delta，所以delta抵消了（也就是可以在股价小幅度波动时免受亏损）。

但是期货无法改变期权空头的gamma风险，所以对于股价大幅度波动带来的亏损无能为力。B选项错误。

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