I hear that option seller can lose unlimited money, but how can option seller lose more than he deposited as margin?
Does he only lose the margin he deposited to sell option or unlimited?
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Let's say I buy an option to buy 100 shares in company A at $1 next month.
Someone sells that option to me, the option seller. They presumably think the company A's share won't appreciate much.
Something extraordinary happens and company A's shares price becomes $1000 or even more at the time the option excise date, there's really no limit to the price a share may reach. Perhaps it's a mining company and they unexpectedly dig up a number of huge diamonds for instance.
I as the buyer of the option choose to exercise my option and buy my 100 shares, paying $100 for them.
Somehow the option seller needs to provide those shares, no matter what price they are now.
Generally your broker won't let things get that bad, they will send you a margin call. If you don't pay that, they will likely close your position and/or sell off any other assets you have with them.
If all that doesn't work, your broker could sue you for the money you still owe. The courts have various means to try to enforce eventual repayment of your debts.
The potential for unlimited losses refers to the option payoff, i.e. market price - strike for a call option. Since there's no limit to how high the market price can go (you could look at Bitcoin, Tesla, or even Amazon as examples), the loss to the option seller is theoretically unlimited.
Contrast that with a short put option, where the loss can still be devastatingly large albeit limited since the stock price is floored at zero.
In practice, you'd get a margin call as soon as your account value drops below the margin requirement, as Robert mentioned.
There is theoretically unlimited loss on any position that represents short the equity position, either direct or derivatively.
The most obvious way is a naked call. The higher the underlying goes, the more the naked call loses.
The second way is a much more unusual and is a bit more complicated:
Exercise By Exception is an OCC rule that states that equity options that are one cent or more in-the-money (ITM) at expiration will be automatically exercised. If you are long the option, you can designate to the OCC via your broker that you do not want your long option to be auto exercised (not applicable to option sellers).
Regular hours market trading ends at 4 PM EST. On the expiration date, options can be exercised until 5:30 PM EST.
A long put gives you the right to sell the underlying at the strike price any time until expiration. If it is out-of-the money at 4 PM and the something causes the stock to drop before 5:30 PM and the put goes ITM, it's likely to be assigned and you'll end up with a short position in the underlying. The resulting short equity position now has directional risk (as an exaggerated example, think FDA drug approval announcement).