There are 3 ways in which it is done in practice:
1) Extrapolation (as you suggest) using a model which factors in 'expected' deviation from vols at t+n based on the normal range of slope between t1 and t2 where t1 is the closest expiry and t2 the next. This may include historical slopes at times when t1 was close to t0 in the expiry cycle. As, in practice, it is always positive this can be done. Simulations which I ran a few years ago showed a low mean error if the slope used in the extrapolation was adjusted dynamically. I wouldn't use this model exclusively in practice though as one could get badly hurt when vol shoots up (or down).
2) Supply and demand. If you generated enough orders on a binary contract you could run it like any other supply / demand driven market matching buyers with sellers and taking some spread. If you did this you wouldn't need an implied vol (though in this instance you could extrapolate one from the prices on the book if you were interested).
3) OTC exotics are aggregated and reported by some parties to aggregation agents like 'Super Derivatives'. I haven't used their service for some time but used to see short term index exotics go through often enough to interpolate a reasonable surface.
In practice I would prefer to use a multi-factor model combining 2 and 3 but if I didn't have 3 I would first elect to use 2 if I had that much liquidity or a combination of 1 and 2 if 3 was unavailable and the liquidity on 2 was not as deep as I would like.
The problem with intraday gold binarys is that you are less likely to get 2 (Gold is traded less by the retail public than the major indices and fx), you probably won't get enough for gold on 3 and 1 has the problems stated.
Intraday implied vol for gold is therefore harder to estimate reasonably than for the more liquid assets on which binary options are sold to the retail masses.
If you have any suggestions on ideas that one might add to 1, 2 and 3 or combine therewith please do let me know.
NQR
