The objectives of this thesis have been to model the spot prices in the energy market, to look at the forward curve, and to derive the Greeks from the spread option. The two energy commodities that have been used are power and gas. Each commodity has been separated into two processes, a stationary and a non-stationary process. The non-stationary process follows a geometric Brownian motion model, while the stationary process follows a CARMA model. The two commodities shared the same non-stationary process and different stationary processes. Cointegration between the two commodities exists, if a linear combination of the (log) prices is stationary. In general, the log commodity spot price dynamics consist of two separate processes; a stationary (short-term) factor and a non-stationary (long-term) factor. In this thesis, the data series for power and gas from the UK energy market have been used. Numerically simulated power and gas data series have also been used. A general data analysis of the two commodities power and gas from the UK energy market in a specific period has been performed. Afterwards, the parameters for the processes have been fitted by using the quadratic covariation method. During this fitting method, most of the parameters of alpha_P and alpha_G have been negative even when the initial values of these parameters were positive. For this reason, the bias has been checked. All the parameters except from the parameter mu was found by the quadratic covariation method, and the Kalman filter was used to find this parameter. Two types of Kalman filters were used. First, the Kalman filter was used for both numerically simulated data series and the UK energy market data series. Second, the Kalman filter was used to calculate the log-likelihood function, with this, the Nelder-Mead maximum method was used to find new parameters. These estimated parameters were again applied to the Kalman filter. This would give an optimized result. The modelled spot prices were used in the forward curve. The probability class Q as a general pricing measure has been introduced. For the measure Q in commodity markets, the mean and the drift, and the autoregressive coefficients in the stationary part have been changed in level. By arbitrage pricing theory in the market, it is free of arbitrage as long as there exists at least one equivalent martingale measure Q. The forward price F_i(t,T) was denoted and calculated. The spread option of the two forward prices with their Greeks has been shown. The spread option in this thesis has been chosen as a variation of the Margrabe formula, and is based on a geometric Brownian motion model.