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How does skew : (25D Put Iv - 25D Call Iv)/50D Iv change with spot? Is there a well defined relationship? And why?

E.g does falling spot increase or decrease skew? How is that change is skew different across expiries (weeklies vs monthlies vs 3 monthlies) etc.

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    $\begingroup$ My 2 cents..no. there is no well defined relationship. It depends on the mkt, the underlying and the circumstance. Each mkt has its own heuristic approaches to what 'should' happen, these are also disproved from time to time. $\endgroup$
    – user68819
    Commented Oct 8, 2024 at 20:38

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From What Does Implied Volatility Skew Measure? - Mixon (2011), it seems that the skew measure you are referring to is inversely related to the spot price (S&P 500 in this case). Take note that the skew measure in Mixon is continuous 30 days TTM (similar to the VIX).

See the figure below for a comparison between Figure 1 in Mixon (2011) and the VIX by CBOE for the duration of Jan 2005 to Jan 2010, which proves that both show a similar pattern and are thus inversely related to the spot (since VIX is well-known to be inverse to the S&P 500 and is used as a hedge for systematic risk ).

You can see that they both spike around the same time below.

enter image description here

enter image description here

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All you want to know and much much more...

https://www.trading-volatility.com/author.html

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    $\begingroup$ While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review $\endgroup$
    – Alper
    Commented 17 hours ago

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