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I am trying to understand the methodology that researchers used to compute ATM-implied volatility with real data.

The problem is giving the discrete sets strike prices of one particular option with one maturity traded on one day, it is quite obvious that we will not have options that are at-the-money (Strike Price = Underlying price). From the set of strike prices and observed option prices (normally the midpoint between best bid/ask price), we can numerically estimate a set of implied volatilities with corresponding strike prices. Then, how could we measure the ATM-implied volatility that usually reported in the academic papers for each maturity on each trading day since we do not have one in the dataset?

Thank you for your time :)

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    $\begingroup$ Usually people do a fit of the data that handles all interpolations. There are a lot of ways to do that, so it is model dependent. The most crude way is to do a linear interpolation between nearest surrounding strikes of the forward, but that is not the best way. If you only need ATM, I feel good about taking the 7 or 8 points nearest to the money and doing a parabolic linear regression with strikes in log-moneyness space. This assumes you have 7 or 8 such points - it is trickier with sparse sets. $\endgroup$ – FinanceGuyThatCantCode May 11 '17 at 20:05

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