We propose a class of alternative stochastic volatility models for electricity prices using the quantile function modeling approach. Specifically, we fit marginal distributions of power prices to two special classes of distributions by matching the quantile of an empirical distribution to that of a theoretical distribution. The distributions from the first class have closed-form formulas for probability densities, probability distribution functions, and quantile functions, while the distributions from the second class may have extremely unbalanced tails. Having rich tail behaviors, both classes allow realistic modeling of the power price dynamics. The appealing features of this approach are that it can effectively model the heavy tail behavior of electricity prices caused by jumps and stochastic volatility and that the resulting distributions are easy to simulate. This latter feature enables us to perform both parameter estimation and derivative pricing tasks based on price data directly observed from real markets.