Mathematical Finance (q-fin.MF)

Abstract: Increased insecurities on the energy markets have caused massive fluctuations of the electricity spot price within the past two years. In this work, we investigate the fit of a classical 3-factor model with a Gaussian base signal as well as one positive and one negative jump signal in this new market environment. We also study the influence of adding a second Gaussian base signal to the model. For the calibration of our model we use a Markov Chain Monte Carlo algorithm based on the so-called Gibbs sampling. The resulting 4-factor model is than compared to the 3-factor model in different time periods of particular interest and evaluated using posterior predictive checking. Additionally, we derive closed-form solutions for the price of futures contracts in our 4-factor spot price model. We find that the 4-factor model outperforms the 3-factor model in times of non-crises. In times of crises, the second Gaussian base signal does not lead to a better the fit of the model. To the best of our knowledge, this is the first study regarding stochastic electricity spot price models in this new market environment. Hence, it serves as a solid base for future research.