Robust Optimization of Portfolio with Stock Options

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Hassanzadeh Mofrad, Maryam | 2010

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 40508 (01)
University: Sharif University of Technology
Department: Industrial Engineering
Advisor(s): Modarres Yazdi, Mohammad
Abstract:
In this thesis, we apply robust optimization to analyze the uncertainty of model parameters of a portfolio optimization which contains stock options. We also develop two robust counterpart models for single period and multiperiod problems. By assuming that the probability distribution of parameters is not known, their uncertainty is considered to lie within known linear intervals. Due to the existence of nonlinear relations (piecewise linear) between uncertain data (stock and option price), we present an over-conservative robust model to make the solution feasible for all parameters. However in the second model by adopting a different approach we develop a robust counterpart model with conservative factor. In the other words, in the second model an investor can adjust the level of risk appropriately. What makes our models distinguished from the previous ones is the way that they encounter nonlinear relations of uncertain parameters. For illustrating the proposed models, three problems with 100 stocks and about 400 options and three problems with 100 stocks and more than 1000 option types for 5 investing period have been generated and run. Finally, we calculate and analyze the results
Keywords:
Financial Engineering ; Portfolio Optimization ; Real Option Method ; Robust Optimization

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