Are financial returns and volatility multifractal at all?

• Název práce v češtině: Jsou finanční výnosy a volatilita skutečně multifraktální?
• Název v anglickém jazyce: Are financial returns and volatility multifractal at all?
• Klíčová slova: ekonofyzika, multifraktalita, finanční trhy, Hurstův exponent
• Klíčová slova anglicky: econophysics, multifractality, financial markets, Hurst exponent
• Akademický rok vypsání: 2013/2014
• Typ práce: diplomová práce
• Jazyk práce: angličtina
• Ústav: Institut ekonomických studií (23-IES)
• Vedoucí / školitel: prof. PhDr. Ladislav Krištoufek, Ph.D.
• Řešitel: skrytý - zadáno vedoucím/školitelem
• Datum přihlášení: 18.06.2014
• Datum zadání: 18.06.2014
• Datum a čas obhajoby: 23.06.2016 11:00
• Místo konání obhajoby: IES
• Datum odevzdání elektronické podoby: 12.05.2016
• Datum proběhlé obhajoby: 23.06.2016
• Oponenti: Mgr. Lucie Kraicová

Seznam odborné literatury

Core Bibliography:
J. Barunik, T. Aste, T. Di Matteo, L. Ruipeng (2012). Understanding the source of multifractality in financial markets. Physica A: Statistical Mechanics and its Applications (17), pp. 4234-4251.
L. E. Calvet, A. J. Fisher (2008). Multifractal volatility: theory, forecasting, and pricing. Amsterdam: Academic Press-Elsevier.
R. Morales, T. Di Matteo, T. Aste (2013). Non-stationary multifractality in stock returns. Physica A: Statistical Mechanics and its Applications (24), pp. 6470-6483.
W.-X. Zhou (2008). Multifractal detrended cross-correlation analysis for two nonstationary signals. Physical Review (0803.2773).
W.-X. Zhou (2009). The components of empirical multifractality in financial returns. EPL (Europhysics Letters) 88.2 (2009): 28004.
W.-X. Zhou (2012). Finite-size effect and the components of multifractality in financial volatility. Chaos, Solitons & Fractals(2), pp. 147-155.

Předběžná náplň práce v anglickém jazyce

Motivation:
The study of financial markets data has become a very attractive and challenging topic. Many studies, that have been devoted to uncover the properties of asset returns over the last 30 years, have brought some fascinating results.
First, the distribution of the returns does not follow normal pattern. Rather, there is excess kurtosis. Second, both first and second moment can be precisely predicted using condition information (Calvet, 2008).
Autoregressive Conditional Heteroskedasticity model (ARCH model) introduced by Robert Engle is considered as one of the most breakthrough approaches devoted to the time-varying volatility. Later on, James Hamilton introduced so called regime-switching model that permits the conditional mean and variance of financial returns to depend on a later state that cannot be observed directly. Based on those, numerous alternative models focusing on the volatility clustering, persistence and its time variation have been established during past years. However, the results on the topic are still quite ambiguous.
The main aim of this thesis will be to analyze whether there is some significant multifractal pattern presented in financial data. We will focus on normalized returns and realized volatility of high-frequency financial data.

Hypothesis:
1.Financial returns do not follow standard-normal distribution (the distribution is skewed and has fat tails), there can be find some multifractal pattern in the data.
2.Normalized returns have more suitable statistical properties for further inference. We suppose that the multifractal pattern will be less significant using normalized data.
3.Bare data on realized volatility shows some presence of multifractality.
4.Bootstrapped data exhibit more unifractal properties.

Methodology:
There are plenty of econometrical models developed in order to investigate multifractal characteristics of time series data. Calvet and Fisher (2008) provide structured review of volatility modeling with a focus on financial applications. Our aim is to choose at least tree appropriate methods which are presented in the book and apply them on selected financial index. The methods will be applied on both, financial returns and realized volatility. For the analysis we will draw the data from the Oxford-Man Institute of Quantitative Finance’s library that provides free data on realized volatility. Our investigation will proceed in several steps. First of all, we will employ the method on the bare data. In the next step, we will normalize the returns in order to support the results on the more suitable data. Shuffling (adjusting data from any auto-correlation pattern preserving their distribution) of the volatility series will clear the data from the effect of long-memory.

Outline:
1.Introduction – basic introduction of financial time series modeling (focused on the returns and volatility). Main statistical properties of the series and its importance for further analysis. Introduction to more complex and non-linear modeling.
2.Literature overview –overview of both the empirical studies on MF in returns/volatility and theoretical framework (focused mainly on the papers presented in Calvet and Fisher (2008).
3.Methodology
a)Long-memory persistence – general framework, main properties and implications for modeling
b)Multifractality – definitions, overview of models and estimations
c)Realized volatility (data cleaning and econometric methods - realized variance, bipower variation)
4.Data description
5.Stating of the main hypothesis and their testing
6.Results and concluding remarks
7.Appendix