 Power put option

A power put has financial payoff $(K-S{)}^n$ below the strike price $K$ and zero at or above it, where $n$ is a positive integer. For $n=1$ this is the ordinary put option. For every $n\ge 1$ the payoff is decreasing and is a convex function of the stock price. A European option permits exercise only at expiry; a perpetual power put option permits exercise at any finite time without a fixed expiry.