Abstarct: We derive semi-analytic solutions for power option prices under the Black-Scholes, generalized Black-Scholes, Heston and double Heston model, respectively; specifically, the pricing formula is shown to be valid whenever the power of the underlying asset price has a finite moment. Unlike the majority of stochastic volatility models, there remains a significant problem to check the existence of moments of assets prices of order higher than one. Fortunately, the moment explosion property under the Heston model is examined. Incorporating with their results, we present explicit formulas for moment generating function of log price and for power option prices under the circumstances when the corresponding moments are finite. In case that the corresponding moment explodes, we provide two numerical methods to derive prices of power put and capped power call options. In spite of a simple idea, numerical examples show that the approximations are extremely accurate and efficient.‏