The right to use a certain amount of capacity in an electrical cable between two countries for the purpose of trading energy is an asset that can be bought. Each hour of capacity can be seen as a real spread option with the energy prices of each country being the underlying processes. In this thesis we build a model to find the fair value of a month of cross-border capacity and use it to predict this value for the Germany-France andNetherlands-Germany border for the months of July-October 2021. Our model is implemented as an IOHMM with 4 states following a multinomial distribution and a non-stationary Normal Inverse Gaussian distribution for each output distribution. We use SPOT prices of each bordering country to create a ’spread process’, which are then used as target values. As inputs various market drivers for each respective country were used. The model produces a mixture probability distribution for the spread for each hour of the month. Taking the discounted expected value then gives the hourly capacity value; certain Greek calculation is also possible. The results show that the capacities follow a comparable trend to the market. The predicted values for September and October fall short of the realized prices; we expect this to be due to unprecedented volatility in the energy market. Finally, we tested whether certain key drivers were mapped to the spreads as one would expect; this was the case for the Dutch and French drivers, but not for the German drivers.

In this paper a two agent wealth distribution model for a closed economic system developed in [2] is presented and extended. We first extend the model by randomly distributing the propensity to save of the agents. We derive a closed form of the stationary relative wealth measure of an agent. We also see that if we take both the propensity to save and the redistribution measure to be uniformly distributed, then the stationary wealth distribution of agent 1 cannot be Beta distributed. Furthermore we conjecture that given a uniform redistribution measure and Beta distributed propensity to save, the resulting wealth distribution cannot be Beta distributed either. The absence of Beta distributions in the wealth distribution shows that there cannot be product stationary measures in these cases. We also extend the model by assuming zero propensity and that the stationary product measure of one agent is conditionally Gamma(α;β)
distributed, where we condition on α be independently distributed as well. We find that the class of distributions for α defined by ψ(α) = α^-k, k an integer always leads to the wealth distribution for agent 1 to be heavy-tailed. We also take steps in showing that there exists a distribution for α that solves for the wealth distribution of agent 1 to be Pareto Lomax distributed.