Derivatives Payoff

Why futures are considered linear while options are considered non linear

Futures and Options are different financial products built to serve different purposes.

Futures - Agreement/Promise between both the parties (buyer & seller). Both of them are contractual obligated to fulfill the agreement. Futures are tradable forward contracts. These are just contracts that are traded and no money is exchanged(except for the MTM)

Options - Options are like insurance, to protect the price (both upside & downside). Only seller is obligated and not the buyer. Options premiums depend on many factors like time to expiry, volatality, rate of interest etc. Here the option buyer pays the cash to buy options contracts(insurance)

This will help give more clarity -