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What Does “Not the Obligation” Mean for an Option Holder?

It means the holder has the choice to exercise the right to buy or sell the underlying asset, but is not required to do so. If exercising the option would result in a loss, the holder can simply let the option expire worthless.

This limits the buyer's risk to the premium paid, providing flexibility.

How Can a Smart Contract Handle the Exercise of an American-Style Option, Which Can Be Exercised Any Time before Expiration?
How Does the Lack of Obligation Differ from a Futures Contract?
How Does the Choice between ASIC and GPU Affect a Miner’s Ability to Switch Coins?
What Is a “Fork Choice Rule” and How Does It Prevent the Nothing-at-Stake Problem?