An Asian surrogate mother. Would this work?

Let's say a black woman (Or any other woman of a non-Asian ethnicity) wanted to have a child, but she was infertile and unable to so she decided to hire a surrogate woman. She had her egg fertilized by her spouse, another black male, and the egg was implanted into the Asian woman who would later have her baby. Would the baby come out black? Would the baby be considered black or Asian?