Once you sell a stock option, you have handed over the rights for the underlying stocks for a specified period to the buyer of the stock option. So no stop losses are possible in a sense that they are possible when you are trading shares alone. However, there are some strategies such as a collar that will enable you to protect your position in case of drastic drops in the stock value.

Even if you have activated an automated stop loss at a given price for your stocks through your brokerage firm, you will still be responsible for providing the underlying stocks if the buyers decides to exercise the stock option. For most people, the brokerage does not allow the stop loss to go through and will override that possibility.

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