No cat goes outside the litterbox except for a good reason. They do not do it 'on purpose'.
First if all, you need to take him to the vet to see if he has a urinary infection, which often causes such behaviour.
If he doesn't have an infection and is just peeing here and there, he is marking his territory, which very often means he is bothered by something, perhaps other cats - inside or outside - or a dog that won't leave him alone, or even human mistreatment. If he is not neutered, and you have it done (a very simple operation), he may well stop. But if your parents and you are not willing to figure it out and make his life less stressful, then it's probably better to re-home him.
PS Your email address will probably be removed for security reasons.