Abstract
Options with non-linear payoffs offer flexibility to investors, but there are few closed formulas known for European options with non-linear payoffs. An adapted decomposition of the payoff can facilitate pricing with closed-form formulas. We show that it is possible to price a polynomial option by expressing it as a combination of several power options with adapted strikes. The general result is independent of the particular dynamics followed by the underlying. Several packages and parabolic calls are studied, along with an example of polynomial options in portfolio selection.