A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 2014. / This dissertation considers the pricing of European and American options.
European option prices are determined by the market and can be veri ed by
a closed-form solution to the Black-Scholes model. These options can only be
exercised at the maturity date. American option prices are not derived from the
market and cannot be priced using the same closed-form solution as in the case
of the European options because American options can be exercised at any time
on or before the maturity date. An initial method was investigated in pricing
a European option but could not price American options. Improvements were
made producing two robust option pricing models. The results of which were
compared to the closed-form solution in the case of European options and
a numerical approximation solution in the case of American options. The
improved models showed two signi cant bene ts. The rst bene t is the ability
to price both European and American options and the second is the ability
to calibrate the models to market prices using market data. Changes to the
parameters of the models showed the limitations of each improved model.
In conclusion, the improved methods are e ective procedures for solving the
European and American option pricing problem.
Keywords: European options, American options, Markov Decision Processes,
Kernel-Based Reinforcement Learning, Calibration.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/15333 |
| Date | 01 September 2014 |
| Creators | Martin, K. S. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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