cambio may mean a bunch of things. If you mean in the verb use: I traded my bike for an IFV because mi neighbour parks all over my mown, yes you can.
Cambiar is used as to swap (sustituir) or to replace (reponer) and to change (as in a lightbulb, you don't replace parts, you "change" them). This sure brings problems if you don't use correctly (giving the appropriate context) because you may have replaced something or installed a different one.
So, in the business of bartering, you also do this, with baseball cards and the like "cambiar", le he cambiado unos cromos a un amigo.
money exchange is also cambiar moneda. But there is no business involved... certainly not in your side.
Regarding the "negocio"; comercio and negocio can be synonyms, but not always. There is no context here, so it can be argued that indeed you can use both, but be careful.
What is wrong with "El oficio"? (not accepted) My understanding was that meant trade/profession. Duolingo if you are listening you should modify this to specify what kind of trade: trade as in trading baseball cards, trade as in trade between countries, trade as in a profession?