Since 1990 many countries have started a deregulation process in the electricity wholesale market with a view to gaining in efficiency, lowering prices and encouraging investments. In most of the markets these objectives have been accomplished, but at the same time, prices have shown high volatility. This is mainly due to certain unique characteristics of electricity as a commodity: it cannot be easily stored; and the flow across lines is dependent on the laws of physics. Electricity must be delivered on the spot to the load.Electricity price variance has been studied very little. Variance is important for constructing prediction intervals for the price. And it is a key factor in pricing derivatives, which are used for energy risk management purposes.A fundamental bid-based stochastic model is presented to predict electricity hourly prices and average price in a given period. The model captures both the economic and physical aspects of the pricing process, considering two sources of uncertainty: availability of theunits and demand. This work is based on three oligopoly models Bertrand, Cournot and Supply Function Equilibrium (SFE) and obtains closed form expressions for expected value and variance of electricity hourly prices and average price.Sensitivity analysis is performed on the number of firms, anticipated peak demand and price elasticity of demand. It turns out that as the number of firms in the market decreases, the expected values increase by a significant amount, especially for the Cournot model. Variances for Cournot model also increase. But the variances for SFE model decrease, taking even smaller values than Bertrand's.Price elasticity of demand severely affects expected values and variances in the Cournot model. So does the firms' anticipated peak demand with respect to full installed capacity in the SFE model. Market design and market rules should take these two parameters into account.Finally, a refinement of the models is used to investigate to what extent prices can be more accurately predicted when temperature forecast is at hand. It has been demonstrated that an accurate temperature forecast can reduce significantly the prediction error of the electricity prices.