Chaos theory and the science of fractals, and their application in risk management

Tania Velásquez

Student thesis: Master thesis

Abstract

Before Chaos Theory consolidated as a main paradigm in science many preconceived ideas had to be modified, in particular, the Newtonian mechanistic perspective of the world characterized by rigid assumptions, mathematical formalism and methodological reductionism. Nevertheless, this change brought great progress for scientific research, as it opened the opportunity to explore the complexity and roughness in natural systems. Unfortunately, financial theories have not evolved at the same pace. Current financial paradigms, based on Neoclassical postulates, are still linked to Newtonian scientific thinking. This has lead financists to address current complexity of financial markets with an inadequate language and method. Therefore, in this investigation, it is proposed to adopt the foundations of Chaos Theory and the Science of Fractals to explain financial phenomena. This will imply a change in the neoclassical notions of rationality, perfect markets and equilibrium models, and the mathematical assumptions of smoothness, continuity and symmetry. With the emergence of this new theory, thus, it would be possible to describe the messiness of today’s financial markets. The key here is to understand the fractal characteristic of the market, as it provides the adequate perspective and mathematical tools to analyze it. Consequently, financial theory will benefit from Chaos Theory and the Science of Fractals in that they will provide more adequate assumptions, and hence, more realistic models of financial behavior. This will be particular important for risk management, as it would allow professionals in this area to understand risk in a more comprehensive manner. Moreover, with the use of fractal statistics, it would be possible to improve financial risk models. To illustrate this point, it would be shown how adopting the hypothesis of this theory in Value-at-Risk, the de facto measure of market risk, may contribute to the enhancement of risk assessment, and even, regulation.

EducationsMSc in Finance and Strategic Management, (Graduate Programme) Final Thesis
LanguageEnglish
Publication date2009
Number of pages79