ETD Collection

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    Optimal Stopping Problems and American Options
    (2006-04-24) Uys, Nadia
    The superharmonic characterization of the value function is proved, under the assumption that an optimal stopping time exists. The fair price of an American contingent claim is established as an optimal stopping problem. The price of the perpetual Russian option is derived, using the dual martingale measure to reduce the dimension of the problem. American barrier options are discussed, and the solution to the perpetual American up-and-out put is derived. The price of the American put on a finite time horizon is shown to be the price of the European put plus an early exercise premium, through the use of a local time-space formula. The optimal stopping boundary is characterised as the unique increasing solution of a non-linear integral equation. Finally, the integral representation of the price of an American floating strike Asian call with arithmetic averaging is derived.
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    American Option Pricing Using Computational Intelligence Methods
    (2006-03-22) Pires, Michael Maio
    An option is the right to buy or sell an underlying asset at a future date by fixing the price now. The field of option pricing produces a challenge because of the complexity with pricing American styled options which cannot be done by the Black-Scholes equations. Neural Networks and Machine Learning techniques are predictors based on past data and it is intuitive to believe that they can model American options as they are non-linear instruments. Call option data on the South African All Share Index (ALSI) was used for testing of the techniques. These two different techniques were compared. What was also done was the comparison of Bayesian techniques applied to both the techniques. What this provided was confidence levels for the predictions. The investigations showed that Machine Learning techniques out-performed Neural Networks. The investigations also showed that there is scope for work to be done to improve the model.