Estimating a two-factor model for the forward curve of electricity

Energy commodity markets have been developing very rapidly in the past few years. Many new products on electricity have appeared and there is a need for a consistent and simple model to price electricity derivatives based on electricity prices and to manage financial risks. In this thesis we addressed the issues of modeling electricity spot and futures prices and prices of options. In Chapter 2 we described the spot market and presented the derivatives traded on electricity markets and over-the-counter operations. We also pointed out the unique features of electricity, such as its non-storability, which makes the pricing and risk management of electricity derivatives more complicated than other financial products. In Chapter 3 we presented an empirical analysis of the spot, futures and options prices available in the German and Dutch electricity markets. In Chapter 4 we pre- sented some classes of existing financial models such as mean-reverting jump di¤usion models, regime-witching models, models with short- and long-term factors which are the most used models for modeling electricity prices and prices of electricity derivatives. As compared with the other financial markets, basic electricity derivatives such as futures and options on futures are more complicated because these products are based not on the spot prices themselves but on the arithmetic averages of the spot prices during the delivery period. In Chapter 5 we extended the two-factor model of Schwartz and Smith [29] by including into the model the possibility to take the averaging of the spot price over the delivery period into account. We derived closed- form solutions for futures, options prices and risk premiums. These pricing formulae depend on the number of parameters; these parameters are the main price drivers and have clear interpretation. These parameters allow us to explain the movements of the prices in the electricity markets and calculate derivatives prices available in the market directly the moment parameters of the models are estimated. We implemented this model for the pricing futures in the German and Dutch elec- tricity markets in Chapter 6 using the Kalman …lter and maximum likelihood technique in order to end the optimal parameters for both markets. We also tested the model with zero correlation between short- and long-term factor and one-factor model. In order to check the effect of introducing CO2 emission permits on the electricity market in 2005, we also tested the model on the restricted information available before and after January 2005. In Chapter 7 we presented the estimated parameters, risk premiums and options prices for different models for both markets. We illustrated how these parameters influence the futures price and risk premiums. We compared the results of one-factor model and model with zero correlation coe¢ cient between short- and long-term factor with modified two-factor Schwartz and Smith model and concluded that the modified two-factor model with averaging over the delivery period performs well especially for capturing the futures prices. The averaging e¤ect allows us to easily incorporate available spot prices in order to calculate the futures prices within the delivery period very precisely. The model performs better and gives clear parameters interpretation when seasonal delivery effect is taken into account.