So I understand that the VIX is an estimate of implied volatility. Volatility can also be calculated from the Black Scholes model. My question is can we use a VIX-like method to calculate implied volatility (of individual equities, not SPY or SPX) and plug that in the B/S model to get a price estimate of the option?
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$\begingroup$ ie, can you 'calculate' how vol should be priced using BSM and use it to determine over/undervalued options? Not successfully, no. Implied vol is also known to be consistently higher than realized vol. $\endgroup$– ChrisCommented Sep 25, 2020 at 2:35
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$\begingroup$ I'm sure you can use that as an estimate for IV, but the question is, what is your goal? Maybe you are looking for a single IV figure that represents the entire SPX curve for an option with about 30 days to expo. I could see that. But for pricing an individual option, you'll have to have real conviction to believe it is priced differently from the current market price., and that using the VIX value for IV is the right IV value. $\endgroup$– confusedCommented Sep 25, 2020 at 5:28
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The VIX methodology is rather involved but in essence it uses all of traded near the money (as it turns out they need not be near the money as long as they are within a continuum of traded options strikes), near dated S&P 500 options to arrive at the VIX (A detailed explanation of the calculation can be found on the CBOE website, http://www.cboe.com/products/vix-index-volatility/vix-options-and-futures/vix-index/the-vix-index-calculation). As such, it is a composite of the implied volatility of short term S&P 500 options.
As there is a skew and term structure of volatility, using such a composite index of a particular equity would not be helpful in pricing individual options. To price individual options, if they are not listed or customized in strike or maturity, the best approach would be to use the closest to the money and maturity of exchange traded options and use an accepted method of interpolating the implied volatilities of said options to arrive at an implied where your customized options may be valued.
