Reinforcement learning applied to option pricing

Martin, K. S.
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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.
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.