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Can a put option and call option be exercised for the same stock with different strike prices?
What you did is called a "strangle." It's rather unlikely that both will be exercised on the same day. But yes, it can happen.  That is if the market is very volatile on a given day, so that the stock hits 13 in the morning, the put gets exercised, and then hits 15 later in the day, so the call gets exercised. Or vice versa. More to the point, the prices are close enough that one might be hit on one day, and the other on a DIFFERENT day. In either case, if one side gets hit, you need to reevaluate your position in the other. But basically, any open position you have can be hit at any time. The only way to avoid this risk is not to have positions.