Parameter estimation of a new energy spot model from futures prices

Abstract

An important issue in the energy market as in the financial market is the parameter estimation of the models representing the dynamics of the spot and the futures. Because one is dealing with unobservable factors, a popular estimation method is the maximum likelihood estimation (MLE), under the assumption that observations are corrupted with additive Gaussian noise. In this framework, the state space representation is used together with the Kalman filtering techniques, and the parameter estimates are obtained through maximization of a likelihood functional. The additional noise in the observation is interpreted to take into account bid-ask spreads, price limits, etc. The argument is clearly forced and unconvincing. The problem is that there is no feedback of the observation noise to the spot price; this leads to a model that is not arbitrage free anymore. The goal of this thesis is two folds: Starting from the two factor model of Schwartz-Smith (2000), we formulate and implement a new arbitrage free model for the futures prices of energy which can be used in a mathematically sound way when estimating the parameter of the model, using the method of maximum-likelihood. In our setup and by using a reverse engineering concept, a new model is developed by perturbing the futures price given by Schwartz-Smith by extra term that takes into account the uncertainties in both the time, and time of maturity, of the term structure of the futures. We ensure that the new model is arbitrage free. As a result of this formulation, the added measurement noise is built in within the model, and the model parameters can be calibrated through the derived likelihood functional without any ad hoc observation noise. The second goal is to estimate the parameters of the new model without any modification to the nonlinear payoff of the futures. For that, we use the particlefiltering algorithm to estimate the parameters. On the empirical side, we identify the parameters of the model using real data from the European energy market.