An option has convexity because of the non-linear relationship between its value and the price of its underlying asset. The option’s value increases or decreases, more proportionately, in reaction to its moneyness when exercised. Convexity of an option represents the effect of change in one variable pertaining to an option, (particularly the out-of-the-money options/ OTM options) where the output changes (the affected variable) in a non-linear way. In options pricing, this cause-effect relationship is known as as gamma (Γ), a greek that captures the sensitivity of the price of an option (option premium) with respect to specific underlying parameters. The convexity notion sometimes refers to the gamma ratio for interest rate options.

Generally, the more out of the money (OTM) an option is, the larger its convexity, and vice versa. An option, by nature, provides capped downside potentiality and unlimited upside potentiality (overall, option leverage). When the underlying moves in-the-money (ITM) at a pace higher than the rate of time decay (theta), the option price (premium) increases in a non-linear fashion.

Convexity is also synonymous with the small adjustment (convexity adjustment) necessary for interest rate derivatives.