Financial modeling and risk measurement on an emerging market using Lévy processes

Programme in Advanced Mathematics of Financial School of Computer Science and Applied Mathematics University of the Witwatersrand, August 2018Efficient financial risk management is fundamental to good business decision making. Risk management heavily relies on the use of mathematical techniques to measure risk; hence it is important to use accurate models when measuring risk. The movement from using models based on geometric Brownian motion is due to its inability to capture many stylized facts of asset returns. Some of the well-known shortcomings of using Brownian motion when modeling asset returns that can be addressed by using Lévy processes include jumps, skewness and heavy tails. This thesis focuses on generalized hyperbolic Lévy processes to model asset returns. The two representations of the generalized hyperbolic distribution (GHD) considered in this thesis are the normal mean variance mixture introduced by McNeil et al. (2005) and the subordinated Brownian motion representation. The results presented in this thesis argue the case for using GHD models to model intraday data to using the normal distribution. The goodness of fit tests performed showed that there were no significant differences between the performance of the two representations of the generalized hyperbolic distribution. Risk measures based on the GHD and normal distribution are defined and evaluated. The results show that the GHD risk measures perform remarkably better than the Gaussian risk measures.XL201