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I'm working with a substantial dataset spanning five years of weekly options data, with records down to the second. My goal is to develop a model that can accurately predict the probability mass function (PMF) of the BSM ATM implied volatility(IV) reaction in 1 day if current IV, current time to expiration(DTE), and percentage change in underlying are given.

Here's where I'm seeking advice: Implied volatility changes vary significantly with DTE, with options nearing expiry showing larger changes compared to those further out.

To address this issue, I'm looking to derive the normalized implied volatility change value for various expiries relative to the percentage change in the underlying asset over 1 day.

After normalizing the implied volatility change, I'll use kernel density estimation (KDE) to build its distribution.

I would greatly appreciate any insights, best practices, or recommendations from experienced practitioners in the field regarding the normalization process.

Thank you all for your time and assistance.

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I did abit of research on normalizing IV, where I used the cross-sectional average of IV among option IVs (with different strike prices). You may also use a time-series average of IVs - like the IV of that option for the past 1 month. Both of these averages can be used to scale/normalize your IV values.

I am not sure if this is the industry way, but there are academics that have used both of these methods that I mentioned above.

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