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Cooljas · 2024年05月12日

完全没看懂,可以再具体解释下吗?

NO.PZ2023091802000212

问题如下:

A manager at an OTC options dealer is reviewing the calculations of an analyst that were used to implement a delta hedge for a long position in a call option. The manager discovers that at the time the hedge was established, the analyst had estimated the delta of the option position as 60,000, but it was really 70,000. If the underlying stock has increased in price since the implementation of the hedge, which of the following statements is correct?

选项:

A.

The value of the option position has increased, but this increase is larger in magnitude than the decrease in value of the stock position used to establish the hedge.

B.

The value of the option position has increased, but this increase is smaller in magnitude than the decrease in value of the stock position used to establish the hedge.

C.

The value of the option position has decreased, but this decrease is larger in magnitude than the increase in value of the stock position used to establish the hedge.

D.

The value of the option position has decreased, but this decrease is smaller in magnitude than the increase in value of the stock position used to establish the hedge.

解释:

A is correct. In order to delta hedge a long call option position, which has a positive delta, the dealer needs to take a short position in the underlying shares, which has a negative delta. If the delta of the option position is miscalculated as lower than its actual delta, then too few shares would be shorted. As a result, the magnitude of the actual delta of the position in the underlying shares is lower than the actual delta of the option position.

If the underlying stock increases in price, the short position in the stock will fall in value and the option position will rise in value. Because its delta is lower in magnitude, the fall in the stock position’s value will be less than the rise in the option position’s value.

B, C, and D are incorrect as per A above.

完全没看懂,可以再具体解释下吗?

1 个答案

pzqa39 · 2024年05月12日

嗨,从没放弃的小努力你好:


这道题考察delta对冲策略,分析师估计该期权头寸的Delta为60,000,但实际上为70,000。如果自从实施对冲以来标的股票的价格上涨,问哪个选项是正确的

 

分析师错误估计了Delta值,他认为是60,000,但实际是70,000。这意味着他认为股票每上升1元,期权价值会增加60,000元,但实际会增加70,000元。

 

因为Delta估计错误,卖出的股票太少,无法完全对冲期权价值的上升。所以,期权价值的上升幅度会大于股票价值的下降幅度。

 

A选项说:“期权头寸的价值增加了,但这种增加的幅度大于用于建立对冲的股票头寸价值的减少。” 这是正确的答案。

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