Option pricing : a particle filtering approach

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October 15, 2015
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Option pricing is a critical issue in the financial market. An investigation into the use of Sampling Importance Resampling (SIR) filter for financial option pricing in the Black-Schole model is performed. The impact of process noise, measurement noise, and the number of particles on the accuracy and performance of SIR filter is examined. The Black-Schole model is solved by the finite difference scheme. The SIR filter is implemented by the use of the GARCH model and the Black-Schole model with synthetic data. The effect of different process noise, measurement noise, and number of particles on the SIR filter was examined. It was found that the SIR filter performed well at lower process noise and high measurement noise when considering profitability of a call option. Also, as the number of particle decrease the SIR filter performed very well.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the Degree of Master of Science in Industrial Mathematics.