This chapter deals with the pricing of certain types of exotic options, called “power options” and “powered options”. The special feature of these contracts is that, compared with plain vanilla options, in the first case the stock price in the payoff function is replaced by the stock price raised to some power, and in the latter case the option payoff is raised to some power. These contracts generalize the special case of a piecewise-linear payoff for plain vanilla contracts. Without loss of generality we only deal with calls, since puts can be priced similarly. If the exponent of a power call option is greater (smaller) than one, the payoff and consequently the price of such contracts is greater (smaller) than the corresponding plain vanilla call option.