How to calculate implied vol for next trading day?

We can seem to get implied vol for a period from now to option expiration, but does anything tell us implied vol for the next trading day ? Like if fomc is tomorrow the next day implied vol would be much higher.

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You can always call your prime broker for an OTC 1-day straddle quote. – Brian B Nov 10 '13 at 3:31

I'm going to start an answer on this and see if it generates discussion:

Firstly you can't get the implied vol to a specific period unless there are options that are liquid and traded around the period you are interested in.

you have four periods of vol, but you don't have listed options between the time periods (usually).

from now until the close of market, from close of market until open of market, from open of market to fomc inclusive, from fomc to next day close.

you might have information about the implied vol from now until close of market today (say there is an expiration on that day) and implied vol from now until close of market tomorrow.

then totalVol = integral(sigma_instantenous(t)^2*dt, 0, T)/T. We can substitute sigma_instantenous(t) = implied vol, then totalVol = impv^2/T. See https://en.wikipedia.org/wiki/Realized_variance

totalSigma(now until eod tomorrow) = impv(now to eod tomorrow)^2*t(now to eod tomorrow) totalSigma(now until eod today) = impv(now to eod tomorrow)^2*t(now to eod tomorrow)

totalSigma from eod today to eodTomorrow = impv(now until eod tomorrow)-impv(now until eod today)

note this period includes both the overnight return and the fomc event. This might give you an idea.

An alternative method is to take the model approach. Fit a model such as sabr to the implied volatility surface, you can interpolate to different time periods. Granted this will likely not nicely take into consideration your fomc event:) See for example http://www.maths.ox.ac.uk/system/files/private/active/0/On%20expansions%20for%20the%20SABR%20model.pdf

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