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Black Swans and fractals: a better way to understand financial markets?

The last decades produced several empirical observations apparently contradicting the main insights of classical finance, suggesting that traditional capital market theory based on the assumptions of rational investors, efficient markets and random walk not always succeeds in properly describing the financial universe. Therefore, the need of a revision of the entire house of modern finance has turned out to be one of the most discussed issues among not only financiers, but also mathematicians and economists.
In such a context, moving from both the powerful instruments and the innovative insights provided by fractal geometry and considering some statistical similarities strictly connecting fractals to financial assets, the goal of my thesis is therefore to propose a possible alternative way to analyse and understand financial markets – that is, the so called hypothesis of fractal markets.
The main milestones of such a revolutionary hypothesis are stable Paretian distribution on the one hand and long-range dependence on the other hand: whereas the former one relates to the peculiar distribution of financial assets returns, thus proposing a specific pattern which differently from the normal distribution contemplates both the leptokurtosis and the heavy tails empirically perceivable in most situations, the latter one refers instead to a peculiar long-term memory effect which biases the way price changes tend to move and fluctuate over time, thus disclaiming the traditional simplifying assumption according to which every event is totally independent of both past and future events. Moreover, such an hypothesis of fractal markets provides a powerful statistical tool, namely the rescaled-range analysis, which can be very helpful to evaluate quantitatively what kind of influence in the financial framework both stable Paretian distribution and long-range dependence actually exercise, manages to explain both the abrupt changes or the discontinuities and the almost-cycles characterising financial assets patterns, associating them to respectively Noah effect and Joseph effect, and includes the concept of multifractal trading time meant as a new dimension, in which the usual clock time can be transformed and from which charts representing financial prices can be generated.
In conclusion, not only having described the main insights proper of the hypothesis of fractal markets from a theoretical point of view, but also having translated them into more practical terms and having carried out some extensive analysis of a few real world situations, what has eventually emerged is that such a way to observe and analyse financial markets, despite not being the absolute Truth, succeeds in offering a much more realistic picture of markets and their risks rather than classical finance and can be therefore considered, answering the question proposed as title of my thesis, Black Swans and fractals: a better way to understand financial markets?, as effectively a better way to understand financial markets.

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- 13 - INTRODUCTION The development of fractal geometry, with the expression fractal appearing for the first time in 1975 in the book entitled Les Objects Fractals: Forme, Hasard et Dimension and written by the great mathematician Benoit Mandelbrot, has represented on the one hand the seeding of a new and innovative perspective from which the entire world can be observed and has contributed on the other hand to the creation of a modern and original system which manages to describe complex shapes, natural forms and real objects in terms of a few simple rules. More specifically, whereas the traditional figures contemplated by Euclidean geometry, namely dimensionless points, one-dimensional lines, two-dimensional planes and three- dimensional solids, despite their being pure, symmetric and smooth, do not succeed in precisely describing the universe around people, rough, asymmetric and subject-to-decay fractals manage instead to deal effectively with all the irregularities observable in nature: therefore, in the same way as Euclidean geometry can be considered as the suitable set of rules to struggle with perfect and ordered frameworks, so similarly fractal geometry can be imagined as the system capable of handling with imperfect and chaotic situations, thus putting itself for being the most appropriate tool in order to successfully cope with the apparently flawed and faulty real world. As a matter of fact, fractals have been always viewed as a powerful new frontier of mathematics which could have turned out to have remarkable implications also in a large number of further sectors and therefore fractal geometry has long since succeeded in capturing the attentions of numerous researchers, from pure mathematicians to natural scientists, with economists and financers included: in particular, these latter ones have tried to extend the main properties and the principal insights behind fractal objects to the financial universe, moving from the belief that since fractal geometry manages to explain and describe some natural, intricate and chaotic phenomena in a much more precise and accurate manner than Euclidean geometry, at the same time it may have put itself for being a much more suitable system to figure out the hidden mechanisms dominating financial assets and the whole world of finance. Based on this latter assumption, the goal of my thesis is therefore to highlight the peculiar connection between fractals and financial assets and to propose a new way to observe,

Tesi di Laurea

Facoltà: Economia

Autore: Davide Pannetta Contatta »

Composta da 137 pagine.

 

Questa tesi ha raggiunto 52 click dal 05/02/2013.

 

Consultata integralmente 2 volte.

Disponibile in PDF, la consultazione è esclusivamente in formato digitale.