Pricing Financial Options Using Ensemble Kalman Filter

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April, 2012
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Pricing financial options is amongst the most important problems in the financial industry. In this study we investigated the use of the ensemble Kalman filter for pricing financial op- tions in the Black-Scholes model. The performance and accuracy of the Ensemble Kalman Filter (EnKF) method based on a Monte Carlo simulation approach for propagation of errors is evaluated on two estimation problems. The first is a synthetic estimation problem using the Van der Pol equation and then a real-world estimation problem concerned with pricing financial instruments. The scenarios considered were to compare effect of different process noise, effect of different measurement noise, and the effect of different ensemble sizes on the performance and accuracy of the EnKF. It was found that as the ensemble size grows the performances of the ensemble Kalman filter improves judging from the values of the root mean square errors. With regard to the process noise, the measurement noise and the initial error covariance, decrease in the value of these parameters actually improves the performance of the EnKF. It was also found that the ensemble Kalman filter approaches same or better accuracy than the extended Kalman filter.
A Thesis submitted to the School of Graduate Studies, Kwame Nkrumah University of Science and Technology, Kumasi, in partial fulfilment of the requirements for the Degree of Master of Philosophy.