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为何不同行权价的布莱克–斯科尔斯隐含波动率不同

文章 Quant Q&A · 作者: M Smith
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总结

本文探讨为何标的资产和到期日相同的期权会呈现不同的隐含波动率。隐含波动率是使选定定价模型能够复现期权报价的波动率输入；它不一定是对某个恒定未来波动率的直接预测。文中示例涉及不同期权的报价，而这些期权通常行权价不同。

回答解释说，布莱克–斯科尔斯模型假设了简化的收益分布和市场环境，包括价格服从对数正态分布；而现实市场可能呈现偏斜和更厚的尾部。因此，不同行权价的价格可能无法由单一布莱克–斯科尔斯波动率拟合；将各个价格代入模型反推时，就会形成波动率微笑或偏斜。讨论还指出，对罕见但代价高昂结果的保护需求可能影响期权价格。本文提供的是定性解释，并未分析所引报价或证明某种特定市场机制。隐含波动率仍取决于模型，文中也未探讨其他定价模型、流动性或买卖价差的影响。

核心观点

  • 隐含波动率是在指定模型下复现期权价格的波动率输入。
  • 标的资产和到期日相同的期权，其隐含波动率也可能因行权价而异。
  • 单一布莱克–斯科尔斯波动率可能无法反映现实收益分布中的偏斜或厚尾。
  • 对低概率、高成本事件的保护需求可能影响期权价格。
  • 此处为定性解释，并未确定任何特定报价模式的成因。

标签

期权波动率衍生品定价市场微观结构
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# Why does the implied volatility on options (with the same underlying and maturity) vary?


# Why does the implied volatility on options (with the same underlying and maturity) vary?












Having studied the basic premises behind option pricing, I thought it would be interesting to look at some real-world options data. I found the following quotes for options on APPL:

https://finance.yahoo.com/quote/AAPL/options?date=1610668800

However, I was surprised to see that the implied volatility for these options varies quite signigicantly, despite having the same underlying and maturity.

Why is this?

## Answer by Bikenfly (score 1)

https://quant.stackexchange.com/a/58578

Bear in mind that the IV you see quoted is Black Scholes IV. The only takeaway can be that the BS model is not the correct model to ACCURATELY price options. Differing IVs are the "fudge" to get better pricing and that option quoting (at the market maker level) really occurs through IV and is just expressed as price. When you look at the assumptions in the BS model, they are AT LEAST the shortcoming of the model (no commissions, continuous price movements, returns are gaussian...) and are return even gaussian? Some research points to that some asset returns are, some returns are more fractal.

## Answer by AlRacoon (score 1)

https://quant.stackexchange.com/a/58579

In short, because 1) the assumption of lognormal returns does not hold in real life--the markets have more skewness and kurtosis and 2) writers of protection want to be compensated more for writing insurance on low probability but high cost events.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: CC BY-SA 4.0 (Stack Exchange)

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。