The initiative by the EU to combat global warming through the introduction of a cap-and-trade system for greenhouse gas emissions in 2005, known as the EU Emissions Trading System (ETS), resulted in the inception of a new financial market. The right to emit one tonne of CO2-equivalents, as well as derivatives on this right, have become commodities, traded both through exchanges and over the counter. A relevant question thus becomes how a market maker trading these derivatives should hedge their exposures. This thesis examines how stochastic optimisation can be used to hedge a portfolio of futures, forwards, and emissions rights in the EU ETS, while taking into account market microstructre effects such as transaction costs. This is done through the implementation of a Stochastic Programming (SP) model that weights portfolio risk against transaction costs,where the entire term structure of futures is Monte Carlo-simulated. The term structure of the futures is analysed by decomposing futures prices into the spot price, the term structure of the risk free interest rate, and the term structure of the convenience yield, as was first done by Working (1948). These are estimated using the non-parametric optimisation framework of Blomvall (2017), where EUROIS contracts and ICE EUA futures are used as benchmark instruments. It was found that the method results in smooth yield curves with small repricing errors, thanks to suitable parameter calibration through 3-fold Cross Validation for both curves. From day-to-day changes in the resulting curves, three systematic risk factors for each curve, that capture more than 98% of the variance during the analysed period from October 2012 to March 2018, were found with PCA. These factors were then fitted to univariate GARCH-models, and normal mixture copulas. This model allows for the hedging problem to be solved with SP. For the out-of-sample period from March 2018 to April 2022, the results show promise, as the portfolios hedged with SP are considerably less volatile than both a statically hedged and an unhedged portfolio. Furthermore, for some values of the parameter weighting risk and costs, these portfolios yield mean variance efficiency.