SUNScholar - Browsing by Author "Le Roux, Christiaan Hugo"

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Levy processes and quantum mechanics : an investigation into the distribution of log returns
(Stellenbosch : Stellenbosch University, 2021-03) Le Roux, Christiaan Hugo; De Wet, Tertius; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
ENGLISH SUMMARY : It is well known that log returns on stocks do not follow a normal distribution as is assumed under the Black-Scholes pricing formula. This study investigates alternatives to Brownian Motion which are better suited to capture the stylized facts of asset returns. Lévy processes and models based on Quantum Mechanical theory are described and t to daily log returns for various JSE Indices. Maximum likelihood estimation is used to estimate the parameters of the Lévy processes and the Cramer-von Mises goodness of t statistic is minimized to estimate the parameters of the Quantum Mechanical models. Q-Q plots and the Kolmogorov-Smirnov t statistic is presented to assess the fit of the various models. The results show that the Lévy processes, specically the Normal Inverse Gaussian process, are the best among the processes considered. The performance of the Quantum Mechanical models could be improved if more eigenstates are considered in the approximation, however the computational expense of these models makes them impractical.