This thesis includes three chapters on electricity and natural gas prices. In the first chapter, we give a brief introduction to the characteristics of power prices and propose a mean reversion jump diffusion model, in which jump intensity depends on temperature data and overall system load, to model electricity prices. Compared to the models used in the literature, we find the model proposed in this chapter is better to capture the tail behavior in the electricity prices. In the second chapter, we use the model proposed in the first chapter to simulate the spark spread option and value the power generations. In order to simulate power generation, we first propose and estimate mean reversion jump diffusion model for natural gas prices, in which jump intensity is defined as a function of temperature and storage. Combing the model with the electricity models in chapter 1, we find that the value of power generation is closer to the real value of the power plants as reflected in the recent market transaction than one obtains from many other models used in literature. The third chapter investigates extremal dependence among the energy market. We find a tail dependence that exceeds the Pearson correlation ρ, which means the traditional Pearson correlation is not appropriate to model tail behavior of oil, natural gas and electricity prices. However, asymptotic dependence is rejected in all pairs except Henry Hub gas return and Houston Ship Channel gas return. We also find that extreme value dependence in energy market is stronger in bull market than that in bear market due to the special characteristics in energy market, which conflicts the accepted wisdom in equity market that tail correlation is much higher in periods of volatile markets from previous literature.