If one's parents give permission for one to do so, then one may. For example, I was asked by my mother to say kaddish for an aunt who died without any children. However, if the parents object, then it is a matter of Kibud Av Ve'Aim (honoring one's parents) because they could regard it as expressing a wish that for them to die. As seen in the sources, it is a requirement that the parents agree before one starts saying the kaddish.
When the parents do consent, it can be considered that one is honoring his parents by doing this. in their stead.
Can I say kaddish for someone if my parents are still alive?
Rabbi Latowicz: if no one else available, and the grandchild's parents consent... then it is ok
Saying Kaddish for a Person Who Does Not Have an Adult Son
The grandson and son-in-law are permitted to say Kaddish only when one
of their own parents is deceased, or if their parents agree to his
reciting Kaddish while they are living. However, someone whose parents are strict that he not say Kaddish while they are both alive may not recite the Kaddish for his grandparent or in-law.