Parchment paper and the broiler do not mix. (Probably wax paper doesn’t mix with the broiler either.)
If something catches on fire in oven, keep oven door closed and turn off the oven! If fire does not die down, calling 911 would be a good thing. Please remember that if a fire extinguisher is NOT nearby, baking soda can help extinguish flames too.
Disclaimer: I am not trained first aid, emergency management or aid of any kind.