i would create vol histogram of the underlying periods, 15day or...for your underlying. Chose a qunatile that's appropriate for your work, and use this volatility. Now vol grows with sqrt of time.

Use that vol, for the relevant payoffs. Global protfolios, also maybe benefit from VIX. Also is not irrational to use mean return=0, if dailly frequency. Cheers Ioannis

If you have lots of historical data, why even consider parametric approaches?

You might use Bootstrap or Filtered Historical Simulation, see http://www.mathworks.com/help/econ/examples/using-bootstrapping-and-filtered-historical-simulation-to-evaluate-market-risk.html

Each one of these would be a reasonable choice.

I recommend to use GARCH models instead of the static Gaussian parametric distribution (times the squared time). In fact, GARCH models allow the fat tails and leptokurtosis that the parametric distribution's don't allow. On the other hand, it has the time as variable, which is the ideal to model n time horizons. With this approach, you can forecast a VaR that it's halfway the 2008 crude oil crash. With a Gauss... no way!

Since the factor (oil) is normal, and portfolio is not, the mapping from the factor to portfolio is non-linear. This fact prohibits calculating factor VaR and mapping it to the portfolio one. You better use any of the mentioned approaches, perhaps historic or Monte Carlo.

Quantitative finance falls within the social sciences, not the physical sciences. Finance is not physics. Therefore, historical data, though extremely helpful, is a frail guide for making financial decisions. As Stephen Covey suggested, "Begin with the end in mind." Why not set up a horse race and see which model is performning best in your context, particularly out-of-sample? Often I have found very simple models with ad hoc adjustments are more accurate out-of-sample (where we all live). The more complicated models often overfit the past that does not reflect the future.

You cannot use the square root of time rule without normality.  Excess kurtosis tends to decline with time aggregation so the square root of time rule is invalid. There is a paper by Danielson and Zigrand on this.

I see some folks confuse Vector Auto Regression with Value At Risk here ... Vadim, I'd go along with Nemanja or Ioannis' suggestion. The square root of time tinkering is valid only under (restrictive theoretically but popular practically) gaussian assumptions. I would go back to the  frequency distributions (eg. Poisson, Neg Bin)  and set the parameter (lambda ?) search from data for those intervals of time you wanted, before convoluting it again with Lognormal (or Pareto if you want fat tail) severity distribution to find Value at Risk.   

Thank you all for your ideas, you have been all of great help!

Ioannis, is there any chance you could contact me directly to provide me with a better inisght over your idea? My email is [email protected]

I would greately appreciate it

If you could use a rolling window with a time horizon suited to the experiment period let me know. You could find the relevant range of your known variable (vols) and also figure out if a tailored set of other macro/portfolio variables work with the data best

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sure, i will.

Hedging: Scaling and the Investor Horizon*, John Cotter and Jim Hanly

Downside risk and the energy hedger's horizon,

Thomas Conlon 1, John Cotter ⁎

Hi, please have a look at our work. I hope it could be of interest...

http://arxiv.org/abs/1408.2462

thx, i will read it!

I sometimes go back to the original data and take the time gap I want to consider for VaR calculation. This is handy if you have enough data.