There are liquid vanilla options trading on an index of 20 equity components.
The question is how to price an option on one of the index components, knowing that there are no options trading on that particular equity, hence no implied volatility available.
Is there any market practice on how to estimate that implied volatility?
My way of doing it would be to estimate beta of the stock to that index, probably with the help of kalman filter, and manipulate beta to get "implied" volatility for the underlying. But maybe there is some better way? I don't want to use any metrics such as historical standard deviation etc. Arch model would be useful to predict "true" future volatility, but I would like to have implied.