Modeling and Calibration of Electricity Price Dynamics for Derivatives Valuation
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The objective of this thesis is to model electricity price dynamics and use the results to valuate derivatives. Electricity prices are known to display features such as spikes, seasonality and jumps, leading to large observations in the spot price. Several studies (Eriksson et al. (2009), Rydberg (1997), N\ae ss et al. (2010)) fit the Normal Inverse Gaussian market model to financial data, comparing favorably to empirical findings in financial markets. This thesis' aims are twofold. Firstly, it seeks to investigate if Normal Inverse Gaussian distributions provide a better fit to electricity data than Normal distributions. We see that it is possible to describe seasonality and trends in the price by a simple deterministic component, while mean reversion is modeled with autoregression dynamics. We are not able, however, to properly recreate spikes or volatility clustering with the model assumed. It follows from the empirical analysis that the Normal Inverse Gaussian distribution provides a considerably better fit to observed residuals than the Normal distribution, allowing higher kurtosis and fatter tails. The second aim of this thesis is to implement a working Path Integration method for forecasting the probability density of the spot price, assuming that the price is sufficiently described by a one-factor model. The results from the Path Integration method are then used for valuing derivatives, and compared with results from Monte Carlo simulations. We calculate the expected derivative values for exercises far in and out of the money, investigating the behavior in thr tail areas of the forecasted price densities. We observe that the implemented Path Integration method estimates much fatter tails than do the estimates from Monte Carlo simulations. This leads to the two methods estimating different derivatives vales. The applicability of the implemented Path Integration method is not certain. Improvements of the implementation in terms of minimizing errors and reducing the run time are subject to further research.