A derivative with a convex payoff-profile at some point before the option's maturity is a simple plan vanilla option. As the option becomes progressively more-in-the money, the rate at which the…

A derivative with a convex payoff-profile at some point before the option’s maturity is a simple plan vanilla option. As the option becomes progressively more-in-the money, the rate at which the position makes money increases until asympathetically approaches the linear payoff of the future. Similarly, as the option becomes progressively more out-of – the money, the rate at which the position loses money decreases until that rate becomes zero. This is an example of: