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carrie_w2008 · 2024年02月14日

选项A怎么理解

NO.PZ2016070202000026

问题如下:

A trader buys an at-the-money call option with the intention of delta-hedging it to maturity. Which one of the following is likely to be the most profitable over the life of the option?

选项:

A.

An increase in implied volatility

B.

The underlying price steadily rising over the life of the option

C.

The underlying price steadily decreasing over the life of the option

D.

The underlying price drifting back and forth around the strike over the life of the option

解释:

D is correct. An important aspect of the question is the fact that the option is held to maturity. Answer A is incorrect because changes in the implied volatility would change the value of the option, but this has no effect when holding to maturity. The profit from the dynamic portfolio will depend on whether the actual volatility differs from the initial implied volatility. It does not depend on whether the option ends up in-the-money, so answers B and B are incorrect. The portfolio will be profitable if the actual volatility is small, which implies small moves around the strike price (answer D).

A 选项是不是也意味着,波动率大,需要不断调整投资组合的头寸导致成本上升~?

2 个答案

pzqa27 · 2024年02月19日

嗨,努力学习的PZer你好:


一级的结论,我们知道波动率和期权价格呈现正相关,那么通过期权实际交易价格用BSM模型反推的隐含波动率自然也是随着价格的上升,反推出的隐含波动率也是上升的。

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pzqa27 · 2024年02月14日

嗨,努力学习的PZer你好:


A的关键点在它说的是隐含波动率,不是真实波动率,的确Delta对冲是个需要不断调整仓位的动态过程。如果标的资产的真实波动率过大,那么每次调整期权数量的幅度就会很大,就会带来很高的调仓成本。因此,真实波动率越小(也就是股票价格围绕着行权价格小幅变动,back and forth around the strike),动态调整成本也越小,即越profitable。

然而A选项说的是implied volatility的增加,implied volatility增加,期权的价值会上升,但问题是这道题说的是to maturity——持有期权到期,所以未到期之前的期权升值跟我们没有什么关系(就是不考虑提前行权)。所以不选A

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carrie_w2008 · 2024年02月15日

老师,请问implied volatility 上升期权价值上升是哪里的知识点,Implied volatility和 realistic volatility 有什么区别

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