Let us say I want to write a naked option on SPX in my interactive brokers margin account. If this is the only position I wish to hold in my account, and I want to use maximum margin, then what is the formula to calculate how many contracts I can write?
Does the answer depend on whether I am writing puts or calls?
Let us assume that SPX is at 2050 and each at the money call/put is 5$. Also assume, my account has 10,000$ in cash and no other position.
Assuming you have a Regulation-T Margin account (portfolio margin would likely penalise you as you would be holding concentrated positions, and the margin calculation is much more complex).
The margin requirement for short index options according to their web page is:
Call Price + Maximum ((15% * Underlying Price - Out of the Money Amount),
(10% * Underlying Price))
= $5 + Maximum( 15% * 2050 - 0 (at the money) , 10% * 2050)
= $5 + Maximum( 307.50, 205.0 )
= $5 + 307.50
= $312.50
Assuming the multiplier is 250, then the margin requirement is $78,125 for a single contract, which well exceeds the $10,000 in cash you have available.
Furthermore, this is the initial margin and also the maintenance margin. So as the prices of the securities change your margin requirements will also change. If you do not have enough, they will liquidate your position.
You might be better of trading a smaller contract, such as options on the SPY ETF, but these have slightly higher margin requirements and are settled in the physical security rather than cash.
The margin requirement for short index options according to their web page is:
Call Price + Maximum ((20% * Underlying Price - Out of the Money Amount),
(10% * Underlying Price))
= $0.50 + Maximum( 20% * 205 - 0 (at the money) , 10% * 205)
= $0.50 + Maximum( 40.80, 20.5 )
= $0.50 + 40.80
= $41.30
With a multiplier of 100, that would be $4,130, so you could sell two option contracts with the $10,000 cash, leaving $1,740 as cushion against future price movements and transaction fees.
