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A Derivative with a Convex Payoff-Profile at Some Point Before

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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 a sympathetically 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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