How do you measure the Accuracy of Implied Volatility?

Recently I've gotten hold of a list or rather a chart of 30-day Implied volatility and historical volatility for the same stock over the course of a year. With these data, I've thought there might be a way to compare these two in order to measure the accuracy of implied volatility and thus the market's accuracy when it comes to individual stocks.

But I've understood that this can be harder than I thought since 30-day Implied volatility refers to calendar days whereas historical volatility is based on business days only, which mixes up the order of every day that otherwise would be equivalent I.e. this day + 30 (for IV 30), would be for HV that day minus everything from around 23 to 19 depending on the presence of non-trading days.

How would you go about if you were tasked to measure the precision of Implied Volatility for a stock? Do you think you could do so efficiently, and if not, how would you make that measurement efficient?

Thank you sooo much to you who took your time to ease my mind! :-)

• iV is not a predictor of HV. Otherwise there wouldn't be a smile in IV. It's a market price for options. Commented Nov 3, 2023 at 18:11
• There is no guarantee that the future follows the same pattern as the past, so no, it isn't predictive. Suggestive, maybe. Commented Nov 3, 2023 at 18:49
• For each strike and maturity there is a different implied volatility. If ATM 1M vol on Apple is ~ 26%, that for 80% moneyness could be +71% (as it was back in this example back in may 2021). Looking at 71% in an isolated manner will tell you close to nothing about the standard deviation (SD) of daily returns (in the future). IV is computed from option prices and the only free parameter in Black Scholes. IV is almost always above RV and there exists a smile to compensate for tail risk and a vol risk premium is paid. Commented Nov 3, 2023 at 19:12
• The thing is that option markets aren't trying to predict HV, IV is a market price for options. And prices are determined by supply and demand and every market maker will demand a mark up. It's their business to earn money, they don't want to just get RV right. It would be like an insurance company pricing their insurance fees so cheap that they just break even in the long run. Commented Nov 3, 2023 at 19:18
• I do not believe you can gain much from pure numerical analysis. The folks over in the Quant stack might disagree with me, but I would recommend actually looking at the companies instead. Or bypassing the whole question and adopting whole-market strategies, diversifying widely rather than trying to outguess everyone else. Commented Nov 4, 2023 at 3:29