Equity Volatility Skew After a Selloff

Summary

This exchange clarifies a statement about how near-dated equity option skew may behave when implied volatility declines after a sudden market drop. The cited explanation assumes low-strike implied volatility stays relatively sticky because it reflects the high realized volatility reached during the selloff. If at-the-money implied volatility then falls while low-strike implieds remain steady, the gap between them widens, so measured downside skew rises during that later decline in volatility.

The questioner reads the passage as describing the initial selloff, when equity prices fall and at-the-money volatility often rises. Under that interpretation, the gap could narrow instead. The answer resolves the apparent conflict by emphasizing the sequence: the statement concerns volatility falling after the sudden decline, not volatility rising during the initial shock. The exchange offers a qualitative interpretation of a passage and its referenced figure, rather than empirical evidence or a general rule for all markets, expiries, or volatility regimes. It does not establish a universal spot-skew correlation.

Key ideas

• The cited skew argument concerns the period after a sudden equity decline, as volatility subsequently falls.
• It assumes low-strike implied volatility is sticky while at-the-money implied volatility declines.
• Under that assumption, the difference between low-strike and at-the-money implied volatility widens.
• The same inference should not be applied to the initial volatility rise during a selloff.
• The explanation is a reading of a specific passage, not a universal empirical law.

Tags

# Does skew flatten with a decline in volatility?


# Does skew flatten with a decline in volatility?












In Trading Volatility by Bennett, he says:

> If there is a sudden decline in equity markets, it is reasonable to assume realised volatility will jump to a level in line with the peak of realised volatility. Therefore, low-strike, near-dated implieds should be relatively constant (as they should trade near the all-time highs of realised volatility). If a low-strike implied is constant, the difference between a low-strike implied and ATM implied increases as ATM implieds falls. This means near-dated skew should rise if near-dated ATM implieds decline (see Figure 103 above).

Doesn't this imply that there is a positive spot-skew correlation? When equities fall, we expect the low-strike implieds to remain relatively constant. However, ATM implied volatility usually goes up when equities fall. Therefore, the difference between low-strike implies and ATM implies will decrease as ATM implies rises (as it does when equities decline).

## Answer by Hans-Peter Schrei (score 3)

https://quant.stackexchange.com/a/74948

The description by Bennett is not very clear, but the reference to the Figure 103 in the text at the end of the paragraph that you cite should resolve the issue.

Bennett is saying that once the sudden equity decline has happened and volatility falls subsequently, ATM implieds fall first with low-strike implieds being sticky. In the figure he is describing the situation when volatility falls, not when volatility rises initially.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.