What would the broker do about this naked call option?
Yes, it can buy back the call, but much before stock hits the $30 mark.   Let us say you got 1$ from selling the call. So the total money in your account is 4$ + 1 $ = 5 $. When stock hits 10$ (your strike), the maintenance margin is 5$. As soon as stock goes past 10, your maintenance margin is violated. So broker will buy back your call (at least IB does that, it does not wait for a margin call). Now if the stock gapped up from 8 to 30,then yes, broker will buy it back at 30, so your account will have a negative balance. Assume the call cost 20$ when stock hit 30, your balance is: 5 - (30-10) = -15. Depending on broker, I suppose they will ask you to bring your account balance back up to positive. If they don't do that, they risk going out of business.
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### Instruction:
What would the broker do about this naked call option?

### Response:
Yes, it can buy back the call, but much before stock hits the $30 mark.   Let us say you got 1$ from selling the call. So the total money in your account is 4$ + 1 $ = 5 $. When stock hits 10$ (your strike), the maintenance margin is 5$. As soon as stock goes past 10, your maintenance margin is violated. So broker will buy back your call (at least IB does that, it does not wait for a margin call). Now if the stock gapped up from 8 to 30,then yes, broker will buy it back at 30, so your account will have a negative balance. Assume the call cost 20$ when stock hit 30, your balance is: 5 - (30-10) = -15. Depending on broker, I suppose they will ask you to bring your account balance back up to positive. If they don't do that, they risk going out of business.