Date

2013

Author

Kalayci, Erkan

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In this thesis, we set up and solved a multi-period stochastic portfolio optimization and hedging model with futures from an airline company's point of view, by taking into account all the specific EU ETS (EU Emission Trading Scheme) regulatory and board-defined trading and risk constraints. That is, in order to hedge the natural physical short position in CO2 emission allowances, we developed an optimal hedging strategy consisting of futures contracts. We thereby successively and comprehensively derived all the mathematical formulations for the system of equations with regard to the specific composition of the profit function and all the underlying real-world constraints in the model. In order to span the space of all possible states, in addition to the modeling of constraints, we also run Monte-Carlo (MC) simulations of correlated geometric Brownian motions (GBM) for traded EUA (EU Emission Allowance) and CER (Certified Emission Reduction) futures prices of different CO2 delivery time periods. Based on the constructed scenario-trees of EUA and CER futures prices and space of feasible states, the optimal buy-hold-sell decision (i.e., futures trading strategy) were determined and the corresponding earnings calculated. Based on the distribution of the revenues, the Value-at-Risk (VaR) measure for the 95% and 99% confidence level was calculated, in order to measure the risk exposure of the portfolio manager. Our contribution to existing academic literature is multiple. As the first ever case, we will apply the multi-stage stochastic programming technique to the aviation sector, which is a brand new included sector within the EU ETS. The methodology and mathematical formulation for the optimization problem including the MC simulated multi-correlated GBMs of EUA and CER financial futures of different CO2 delivery time periods and the resulting system of equations have been self-developed. That is, the consideration of all the actually valid EU ETS regulatory and real-world oriented, managerial, trading constraints in the airline sector, makes our model to a real-life application, which in the constellation and idea, set up in this thesis, has not been applied in academic research before. Hence, the developed methodology in thesis could be widely used implemented, adapted and extended to other academic problems and practical applications. The thesis ends with a conclusion and outlook to future studies.

Subject Keywords

Mathematical optimization., Stochastic processes., Monte Carlo method.

URI

http://etd.lib.metu.edu.tr/upload/12616326/index.pdf
https://hdl.handle.net/11511/22852

Collections

Graduate School of Applied Mathematics, Thesis