The last and equally important diplomatic option is trade.
Trade is divided into several parts. You can send or receive a given amount of gold from another faction as a one-time or long-term payment. This similarly with food - you can send a certain amount of food to another faction throughout X number of turns, or get it from another faction. The third option is to trade items - weapons, armor, mounts, supporters, or accessories - in exchange for influence, gold, or pushing through other diplomatic options.
The fourth and separate issue is exchange. You exchange one good (grain, rice, iron, jade, silk, etc.) to get another from the other faction - this will result in a large increase in the gold received each turn. This is also the option with the most restrictions - the number of trade exchange offers depends on the development of the faction (level, built buildings, as well as assigned posts in the court). You can exchange goods only with factions you can access directly (their border is next to yours, or when you are able to access them through the territory of an ally).