I'm familiar with GARCH. It does a somewhat acceptable job at estimating future volatility on daily bars.

Let's say I have a very long history of 1min bars of say USD/JPY. Now, we know that there are certain hours of the day when this will be much more volatile. We also know that the market will go through days or weeks where it will be more or less volatile.

Is there a usual or conventional method which people use to estimate the future volatility over the next say two hours? Another way of asking the same question is, how would I price an at the money call option on USD/JPY which expires in two hours time from now (based on a history of minute bars)?

Note: I am assuming that I don't have access to the market implied volatilities.

If you want to stay close to GARCH type of models then adding indicator variables like "is office hour" to the model would work. I would try multiplicative factors, eg office hour vol is 20% higher than other hours vol, resulting in either a factor 1 or 1.2. (The 1.2 would be the number you need to calibrate). This is closely related to logistic regression where you model something as exp(a.x +b) with x your factor values (taking values 0 or 1) and a and b a vector and a scalar you need to calibrate.

Thanks @outrun. Usually in currency markets between different timezones you get a bit of a double hump on trading volume (a proxy for volatility in some senses).

Let's say we head down your route and say that we are going to simplify this to just two regimes, 'office hours' and 'not office hours'. That may be 8h of the day we expect the currency to be 1.2x more volatile than the other 16h of the day. How should I create a rolling measure? For example I've just finished an 8h office day and I'm now 1h into the next 16h out of office hours. When i look at the preceding 8h, should I be summing squared price changes on each minute bar, or should I be looking at the price change over the whole of the 8h? Clearly if there is a momentum effect or mean reversion then the two will not convert to the same volatility over a constant period. However, we are now 1h into the next regime. How do I combine 1h of this regime with the 8h before that and the 16h before that etc?

I'm thinking of using some type of weighting curve (by time of day) and rolling average where less volatile times of days count more. The problem with this is that small bumps at non-volatile times of day may lead to outsized changes on volatiltiy.

I see the CBOE has a JYVIX -- probably sub-optimal not to include this as an exogenous term in the GARCH eqn or otherwise make use of it. Ditto for any other forward-looking info that seems significant.

..yes, let's try! It's probably the simplest extension to GARCH?

Using this notation I found on wikipedia,
[$]y_t=x'_t b +\epsilon_t[$]

[$]\epsilon_t| \psi_t \sim\mathcal{N}(0, \sigma^2_t)[$]

[$]\sigma_t^2=\omega + \alpha_1 \epsilon_{t-1}^2 + \cdots + \alpha_q \epsilon_{t-q}^2 + \beta_1 \sigma_{t-1}^2 + \cdots + \beta_p\sigma_{t-p}^2 = \omega + \sum_{i=1}^q \alpha_i \epsilon_{t-i}^2 + \sum_{i=1}^p \beta_i \sigma_{t-i}^2[$]


I would put a deterministic time varying [$]f_t = \{0,1\}[$] factor here:
[$]\epsilon_t| \psi_t \sim\mathcal{N}(0, \sigma^2_t e^{c f_t })[$]

That way you can (I expect) nicely handle the regime switches and the rolling measure? [$]\sigma[$] could be thought of as an base vol, which gets scales by deterministic intra-day and weekly factors.


About Alan's idea for exogenous variables: I would try that too. The only issue I had is that if that exogenous variable moves on your timescale then 
you will have to model the dynamics of that too if you want to do e.g. multi-step MC simulations.

For the USDJPY intraday, I would define moments of sharp increases in volatility, followed by a periods of gradual, slow decrease.
Those moments occur at the open of the Asian and American sessions, and when important news come out.
I think using scheduled times for the major financial news such as NFP or Fed rate to model currencies volatility is crucial. Volatility in NFP Friday is very different than other Fridays.

I share with TraderWalrus referring to the markets to operate this pair USD/JPY, since in those trading timing this pair shows more movement and that is what we are looking for. It is for this reason also that some strategies are mainly made for the period of time when both markets converge