A payoff (of some derivative instrument) whose amount is a convex function of the value of the underlying instrument. Generally, it is an option-like payoff, where the compensation is asymmetric: the holder would share the upside but would not incur direct losses on the downside. In other words, on the upside the payoff of the instrument is more or less proportional to the change in the instrument’s value (price). However, on the downside, the losses in the payoff would be way less proportional to the losses in the instrument’s value (price).

In concept, a convex payoff is similar to the status of limited liability.