It has already been answered why margin exists and roughly how it calculated. "Options on futures employ an entirely different method known as SPAN margining", which is basically CME Group's take on a multi-scenario weighted conditional VaR. I will attempt to provide additional insight on the other part of the question as to why IB's margin requirements on future options are excessive.
IB's requirements are indeed excessive. In fact, as you point out, they are almost triple the risk (\$562.5) for an initial position (\$1575) and double for maintenance (\$1056). This exceeds the margin requirements imposed by the CME Group :
Long option value is always greater than the span risk that is
calculated because we understand that you cannot lose more than what
you have paid for a long option.
It has also been proposed that this could be due to futures settlement. This also is not true. According to the product specs, e-Mini S&P Futures are cash settled. Moreover, the numbers you are given do not jive with the margin requirements for S&P E-mini Futures:
...nor those margin requirements provided by IB:
In my mind, there are two possible reasons that IB would impose excessive margin requirements:
- Unintended error on behalf of the software/risk folks (e.g., bungling algorithm)
- Intentional risk gouging to discourage risk taking and/or to increase IB's cash reserves
The only way to be sure what is going on is to call IB's risk management office. From my experience, unless you are an institutional client, you will be put on hold for a long time.