Technically your personal items and liability would be covered under your parents' homeowners insurance
policy while you live under their roof. However, if you had to file a claim you would be doing so under their policy. This could have negative consequences for your parents since almost any claim filed on their policy could cause their rate to increase or their company to no longer want to insure them. I would recommend getting your own separate renters insurance
policy to cover your personal belongings so that, worst case scenario, you could file a claim under your own policy without affecting your parents' policy. Once you move out to your own place it's very simple to update the home address listed with your provider.