This thesis explores and compares the usual mathematical models, namely Geometric Brownian Motion, Uhlenbeck-Ornstein process and Uhlenbeck-Ornstein process with the presence of jumps, deployed for quantitative analysis, Derivative Valuation and Risk Management of electricity derivatives. It provides for the mathematical justification of these models and discusses about their potential applicability. A new model is proposed that investigates and brings into perspective the process of power price generation and the electricity Supply Stack. Analysis is conducted about electricity demand and its statistical properties. Calibration routines such as Maximum Likelihood Estimation, the Method of the Least Squares, Regression Analysis and the intuitive Recursive Filter are established, compared and discussed for the relevant models in this Thesis. We discover that Maximum Likelihood Estimation fails to capture the fat tailed electricity price distribution as satisfactorily as the Recursive Filter for UKPX Base power prices. The models are assessed on Vanilla, Spread, Asian as well as other Electricity Derivatives prices and on practical Credit Risk metrics. We discover that the Supply Stack Option Valuation performance is superior to the traditional models, compared on limited quoted option prices. From a Credit point of view the Out of the Money options are considered more risky as far as the Stack model is concerned while for In the Money and At the Money options the stack model on average demonstrates lower risk. Finally, we conclude about the merits and limitations of the supply stack model both on qualitatively and quantitatively grounds.