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:
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