One of the things we've come to know about asthma is that it can be inherited from one or both parents. So, your suggestion may be right.
The chances of a child having asthma increases when one or both parents have an history of the illness. The chances are more pronounced if both parents have the illness than when one parent does.
Asthma can be triggered by series of factors and while some people develop asthma later on in life, it is not uncommon to see children suffering from the disease. However, I would like to point out that it is not as simple as just expecting a child to have asthma because the parent has it. There are certain factors that would have to be put into consideration for this to happen.
We have also seen instances where one child among a twin would have asthma and the other would not. The chances of a child also inheriting asthma from a parent is one out of three so you see here that it is not a given that if one's parents has the disease that it will necessarily show up in the child.
Also, the longevity of the illness may differ from individual to individual. While some people experience cessation in the illness after the contributing factors might have been eliminated, some continue to experience it even after the contributing factor has been removed.
I once had an aunt that was asthmatic and trust me, the experience isn't one I'd wish for anybody. It stresses not just the individual but those around them.
It is but it doesn't follow that once you parents have asthma, you'll get one too. Your risk of having it would be higher compared to having progenitors without the condition.