If you have asthma, it's not a sure thing that your child will have it, too. While we know that having a parent with asthma is a risk factor for developing asthma, scientific studies vary with regards to the exact likelihood.  Also, it seems that the environment is very important.  In studies of identical twins, who both have the same genetic make-up and were raised in different environments, there were cases in which one twin developed asthma while the other did not.  So both your genes and what you are exposed to in your environment play key roles.