The overall purpose of this thesis is to find an optimal portfolio with American options and European options, which minimizes the risk associated with the portfolio and satisfies a certain level of expected return and constrained budget. The design of the Nonlinear programming model is based on Harry Markowitz and William Sharpe’s Portfolio Theory, and their model for portfolio selection. This procedure includes a Single-Option model and a Multiple-Options model, which solve for the number of option contracts that need to be included in the portfolio. The conduction of sensitivity analysis on the budget, acceptable expected return, risk and return implies that option portfolio selection is more susceptible to the change of risk. In this thesis, I find that American options are more risky and costly than European options, so investors should put more money in purchasing European options to minimize their risks based on my model.


Morrison, Jillian




Finance and Financial Management | Non-linear Dynamics | Numerical Analysis and Computation | Portfolio and Security Analysis


Nonlinear programming, Newton's method, American and European options, portfolio selection, Kuhn-Tucker conditions

Publication Date


Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis



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