An Investigation into Variations of Brownian Motion: Towards a Deeper Understanding of Financial Asset Pricing
PhD Thesis
Shakeel, M. (2019). An Investigation into Variations of Brownian Motion: Towards a Deeper Understanding of Financial Asset Pricing. PhD Thesis https://doi.org/10.18744/lsbu.883y7
Authors | Shakeel, M. |
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Type | PhD Thesis |
Abstract | Modelling the asset returns distribution has been the focal point of modern finance for almost a century. The extensively studied and applied Geometric Brownian Motion (GBM) modelling process provides the returns distribution to asset prices which is normally distributed. However historical asset returns are skewed and possess excess kurtosis, indicating that a returns distribution has a thicker tail when compared with the normal distribution. Numerous alternate distributions have been proposed to model asset returns, however these distributions are imposed on data exogenously with complex equations for parameter estimation. This innovative research modifies the GBM model by embedding an extra factor to capture leptokurtosis of historic data. This extra factor incorporates a weighting factor and a stochastic function modelled as a mixture of power and trigonometric functions. Simulations based on this Modified Brownian Motion Model with optimal weighting factors selected by goodness of fit tests, substantially outperform the basic GBM model in terms of fitting the returns distribution of historic data price indices. Furthermore this research provides an interpretation of the additional stochastic term in relation to irrational behaviour in financial markets. An innovative extension of Geometric Brownian Motion model is developed by incorporating a weighting factor and a stochastic function modelled as a mixture of power and trigonometric functions. Simulations based on this Modified Brownian Motion Model with optimal weighting factors selected by goodness of fit tests, substantially outperform the basic Geometric Brownian Motion model in terms of fitting the returns distribution of historic data price indices. Furthermore we attempt to provide an interpretation of the additional stochastic term in relation to irrational behaviour in financial markets and outline the importance of this novel model. |
Year | 2019 |
Publisher | London South Bank University |
Digital Object Identifier (DOI) | https://doi.org/10.18744/lsbu.883y7 |
File | License File Access Level Open |
Publication dates | |
Online | 20 Aug 2019 |
Publication process dates | |
Deposited | 15 Oct 2019 |
https://openresearch.lsbu.ac.uk/item/883y7
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