I'm talking practically. For example: Suppose I write 10 contracts with strike $102 for 50 cents an option, with expiry two weeks from now, with stock price at $100. A week from now stock hits, say, 102.25. Can I expect to be required (forced) to settle this position at any time from a week from now to two weeks from now, or do I chose when I get to settle the position? I'm currently experimenting with option in StockTrak, and I wanna know what happens in this case when I start betting with real money...
Yes, if it's an American style option. American style options may be exercised at any time prior to expiration (even if they're not in-the-money). Generally, you are required to deliver or accept delivery of the underlying by the beginning of the next trading day.
If you are short, you may be chosen by the clearinghouse to fulfill the exercise (a process called "assignment"). Because the clearinghouse is the counter-party to every options trade, you can be assigned even if the specific person who purchased the option you wrote didn't exercise, but someone else who holds a long position did. Similarly, you might not be assigned if that person did exercise. The clearinghouse randomly chooses a brokerage to fulfill an assignment, and the brokerage will randomly choose an individual account.
If you're going to be writing options, especially using spreads, you need to have a plan ahead of time on what to do if one of your legs gets assigned. This is more likely to happen just before a dividend payment, if the payment is more than the remaining time value.