# Tiziana Di MatteoKing's College London | KCL · Department of Mathematics

Tiziana Di Matteo

## About

151

Publications

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5,865

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Introduction

Additional affiliations

January 2002 - December 2008

## Publications

Publications (151)

Pricing derivatives goes back to the acclaimed Black and Scholes model. However, such a modelling approach is known not to be able to reproduce some of the financial stylised facts, including the dynamics of volatility. In the mathematical finance community, it has therefore emerged a new paradigm, named rough volatility modelling, that represents...

Pricing derivatives goes back to the acclaimed Black and Scholes model. However, such a modeling approach is known not to be able to reproduce some of the financial stylized facts, including the dynamics of volatility. In the mathematical finance community, it has therefore emerged a new paradigm, named rough volatility modeling, that represents th...

The analysis of multidimensional data is becoming a more and more relevant topic in statistical and machine learning research. Given their complexity, such data objects are usually reshaped into matrices or vectors and then analysed. However, this methodology presents several drawbacks. First of all, it destroys the intrinsic interconnections among...

Research on scaling analysis in finance is vast and still flourishing. We introduce a novel statistical procedure based on the generalized Hurst exponent, the Relative Normalized and Standardized Generalized Hurst Exponent (RNSGHE), to robustly estimate and test the multiscaling property. Furthermore, we introduce a new tool to estimate the optimal...

The dynamical evolution of multiscaling in financial time series is investigated using time-dependent Generalized Hurst Exponents (GHE), Hq, for various values of the parameter q. Using Hq, we introduce a new visual methodology to algorithmically detect critical changes in the scaling of the underlying complex time-series. The methodology involves...

The dynamical evolution of multiscaling in financial time series is investigated using time-dependent Generalized Hurst Exponents (GHE), $H_q$, for various values of the parameter $q$. Using $H_q$, we introduce a new visual methodology to algorithmically detect critical changes in the scaling of the underlying complex time-series. The methodology i...

Multilayer networks proved to be suitable in extracting and providing dependency information of different complex systems. The construction of these networks is difficult and is mostly done with a static approach, neglecting time delayed interdependences. Tensors are objects that naturally represent multilayer networks and in this paper, we propose...

Composite development indicators used in policy making often subjectively aggregate a restricted set of indicators. We show, using dimensionality reduction techniques, including Principal Component Analysis (PCA) and for the first time information filtering and hierarchical clustering, that these composite indicators miss key information on the rel...

The analysis of multidimensional data is becoming a more and more relevant topic in statistical and machine learning research. Given their complexity, such data objects are usually reshaped into matrices or vectors and then analysed. However, this methodology presents several drawbacks. First of all, it destroys the intrinsic interconnections among...

Scaling and multiscaling financial time series have been widely studied in the literature. The research on this topic is vast and still flourishing. One way to analyse the scaling properties of time series is through the estimation of scaling exponents. These exponents are recognized as being valuable measures to discriminate between random, persis...

Systemic liquidity risk, defined by the IMF as "the risk of simultaneous liquidity difficulties at multiple financial institutions", is a key topic in macroprudential policy and financial stress analysis. Specialized models to simulate funding liquidity risk and contagion are available but they require not only banks' bilateral exposures data but a...

We find a nonlinear dependence between an indicator of the degree of multiscaling of log-price time series of a stock and the average correlation of the stock with respect to the other stocks traded in the same market. This result is a robust stylized fact holding for different financial markets. We investigate this result conditional on the stocks...

Among several developments, the field of Economic Complexity (EC) has notably seen the introduction of two new techniques. One is the Bootstrapped Selective Predictability Scheme (SPSb), which can provide quantitative forecasts of the Gross Domestic Product of countries. The other, Hidden Markov Model (HMM) regularisation, denoises the datasets typ...

In this review article we present some of achievements of econophysics and sociophysics which appear to us the most significant. We briefly explain what their roles are in building of econo- and sociophysics research fields. We point to milestones of econophysics and sociophysics facing to challenges and open problems.

Among several developments, the field of Economic Complexity (EC) has notably seen the introduction of two new techniques. One is the Bootstrapped Selective Predictability Scheme (SPSb), which can provide quantitative forecasts of the Gross Domestic Product of countries. The other, Hidden Markov Model (HMM) regularisation, denoises the datasets typ...

We introduce a multistep-ahead forecasting methodology that combines empirical mode decomposition (EMD) and support vector regression (SVR). This methodology is based on the idea that the forecasting task is simplified by using as input for SVR the time series decomposed with EMD. The outcomes of this methodology are compared with benchmark models...

We find a nonlinear dependence between an indicator of the degree of multiscaling of log-returns time series of a stock and the average correlation of it with the other stocks traded in the same market. This result is a robust stylized fact holding for different financial markets. We investigate the relationship of this result with the stocks' capi...

We introduce a new factor model for log volatilities that performs dimensionality reduction and considers contributions globally through the market, and locally through cluster structure and their interactions. We do not assume a-priori the number of clusters in the data, instead using the Directed Bubble Hierarchical Tree (DBHT) algorithm to fix t...

We investigate how efficiently a known underlying causality structure of a simulated multivariate process can be retrieved from the analysis of time-series. Causality is quantified from conditional transfer entropy and the network is constructed by retaining only the statistically validated contributions. We compare results from three methodologies...

We investigate how efficiently a known underlying sparse causality structure of a simulated multivariate linear process can be retrieved from the analysis of time series of short lengths. Causality is quantified from conditional transfer entropy and the network is constructed by retaining only the statistically validated contributions. We compare r...

We propose here a multiplex network approach to investigate simultaneously different types of dependency in complex data sets. In particular, we consider multiplex networks made of four layers corresponding respectively to linear, non-linear, tail, and partial correlations among a set of financial time series. We construct the sparse graph on each...

The Empirical Mode Decomposition (EMD) provides a tool to characterize time series in terms of its implicit components oscillating at different time-scales. We apply this decomposition to intraday time series of the following three financial indices: the S\&P 500 (USA), the IPC (Mexico) and the VIX (volatility index USA), obtaining time-varying mul...

We propose a method to measure the Hurst exponents of financial time series. The scaling of the absolute moments against the aggregation horizon of real financial processes and of both uniscaling and multiscaling synthetic processes converges asymptotically towards linearity in log-log scale. In light of this we found appropriate a modification of...

We investigate Bitcoin network monitoring the dynamics of blocks and transactions. We unveil that 43\% of the transactions are still not included in the Blockchain after 1h from the first time they were seen in the network and 20\% of the transactions are still not included in the Blockchain after 30 days, revealing therefore great inefficiency in...

The authors describe blockchain’s fundamental concepts, provide perspectives on its challenges and opportunities, and trace its origins from the Bitcoin digital cash system to recent applications.

We report significant relations between past changes in the market correlation structure and future changes in the market volatility. This relation is made evident by using a measure of “correlation structure persistence” on correlation-based information filtering networks that quantifies the rate of change of the market dependence structure. We al...

We measure the influence of different time-scales on the intraday dynamics of financial markets. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying measures of complexity: 1) an amplitude scaling exponent and 2) an entropy-like measure. We apply these...

We discuss two elements that define the complexity of financial time series: one is the multiscaling property, which is linked to how the statistics of a single time-series changes with the time horizon; the second is the structure of dependency between time-series, which accounts for the collective behaviour, i.e. the market structure. Financial t...

We discovered that past changes in the market correlation structure are significantly related with future changes in the market volatility. By using correlation-based information filtering networks we device a new tool for forecasting the market volatility changes. In particular, we introduce a new measure, the "correlation structure persistence",...

We introduce a methodology to construct sparse models from data by using information filtering networks as inference structure. This method is computationally very efficient and statistically robust because it is based {on} local, low-dimensional, inversions of the covariance matrix to generate a global sparse inverse. Compared with state-of-the-ar...

We discuss the origin of multiscaling in financial time-series and
investigate how to best quantify it. Our methodology consists in separating the
different sources of measured multifractality by analysing the
multi/uni-scaling behaviour of synthetic time-series with known properties. We
use the results from the synthetic time-series to interpret t...

We measure the influence of different time-scales on the dynamics of
financial market data. This is obtained by decomposing financial time series
into simple oscillations associated with distinct time-scales. We propose two
new time-varying measures: 1) an amplitude scaling exponent and 2) an entropy
like measure. We apply these measures to intra-d...

We empirically analyze the most volatile component of the electricity price
time series from two North-American wholesale electricity markets. We show that
these time series exhibit fluctuations which are not described by a Brownian
Motion, as they show multi-scaling, high Hurst exponents and sharp price
movements. We use the generalized Hurst expo...

We establish a formal connection between algorithmic correspondence theory and certain dual characterization results for finite
lattices, similar to Nation’s characterization of a hierarchy of pseudovarieties of finite lattices, progressively generalizing
finite distributive lattices. This formal connection is mediated through monotone modal logic....

Volatility of intra-day stock market indices computed at various time
horizons exhibits a scaling behaviour that differs from what would be expected
from fractional Brownian motion (fBm). We investigate this anomalous scaling by
using Empirical Mode Decomposition (EMD), a method which separates time series
into a set of cyclical components at diffe...

The evolution with time of the correlation structure of equity returns is
studied by means of a filtered network approach investigating persistences and
recurrences and their implications for risk diversification strategies. We
build dynamically Planar Maximally Filtered Graphs from the correlation
structure over a rolling window and we study the p...

We quantify the amount of information filtered by different hierarchical clustering methods on correlations between stock returns comparing it with the underlying industrial activity structure. Specifically, we apply, for the first time to financial data, a novel hierarchical clustering approach, the Directed Bubble Hierarchical Tree and we compare...

We report evidence of a deep interplay between cross-correlations hierarchical properties and multifractality of New York Stock Exchange daily stock returns. The degree of multifractality displayed by different stocks is found to be positively correlated to their depth in the hierarchy of cross-correlations. We propose a dynamical model that reprod...

We introduce a methodology to efficiently exploit natural-language expressed biomedical knowledge for repurposing existing drugs towards diseases for which they were not initially intended. Leveraging on developments in Computational Linguistics and Graph Theory, a methodology is defined to build a graph representation of knowledge, which is automa...

We quantify the amount of information ltered by dierent hierarchical clustering methods on correlations between stock returns comparing the clustering structure with the underlying industrial activity classication. We apply, for the rst time to nancial data, a novel hierarchical clustering approach, the Directed Bubble Hierarchical Tree and we comp...

We introduce the concept of {\it self-referential order} which provides a way
to quantify structural organization in non crystalline materials. The key idea
consists in the observation that, in a disordered system, where there is no
ideal, reference, template structure, each sub-portion of the whole structure
can be taken as reference for the rest...

Risk is not uniformly spread across financial markets and this fact can be exploited to reduce investment risk contributing to improve global financial stability. We discuss how, by extracting the dependency structure of financial equities, a network approach can be used to build a well-diversified portfolio that effectively reduces investment risk...

We perform an extensive empirical analysis of scaling properties of equity
returns, suggesting that financial data show time varying multifractal
properties. This is obtained by comparing empirical observations of the
weighted generalised Hurst exponent (wGHE) with time series simulated via
Multifractal Random Walk (MRW) by Bacry \textit{et al.} [\...

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, to characterize, and to simulate networks with a broad range of properties. Any network can be embedded on a surface with sufficiently high genus and therefore the study of topologically embedded graphs is non-restrictive. We show that the local propertie...

In many practical applications, correlation matrices might be affected by the “curse of dimensionality” and by an excessive sensitiveness to outliers and remote observations. These shortcomings can cause problems of statistical robustness especially accentuated when a system of dynamic correlations over a running window is concerned. These drawback...

We propose a unified model to build planar graphs with diverse topological characteristics which are of relevance in real applications. Here convex regular polyhedra (Platonic solids) are used as the building blocks for the construction of a variety of complex planar networks. These networks are obtained by merging polyhedra face by face on a tree-...

We introduce a graph-theoretic approach to extract clusters and hierarchies in complex data-sets in an unsupervised and deterministic manner, without the use of any prior information. This is achieved by building topologically embedded networks containing the subset of most significant links and analyzing the network structure. For a planar embeddi...

The file PaperSupporting_ver230112_PLoSOne.pdf contains additional information to the manuscript explaining methods, procedures and results in further details. It consists of 16 pages, 3 tables and 11 figures.
(PDF)

The file DHBT_codesAndData.zip is a compressed achieve file containing the matlab code DBHT.m to compute the DBHT clusters and hierarchies, this code calls 8 other functions: BubbleCluster8.m, CliqHierarchyTree2.m, BubbleCluster8.m, clique3.m, cRand1.m, DirectHb.m, doPMFG.m, DrawPMFG.m. The achieve also contains the code iris_demo.m and the data ma...

In order to investigate the flux line dynamic in the recently discovered MgB2 superconductor, we have measured the ac magnetic susceptibility as a function of the temperature T and the ac field frequency f on a bulk sample. In particular we have analysed the fundamental and the third harmonics χ1,3(T) = χ′1,3(T) + iχ′′1,3(T) by comparison of the ex...

The two-dimensional negative-U Hubbard model is studied by means of the composite operator approach. In a generalized mean-field approximation we calculate different quantities, as the chemical potential, the double occupancy, the static uniform spin magnetic susceptibility and the density of states for various values of the particle density, attra...

In this paper, we use the generalized Hurst exponent approach to study the
multi- scaling behavior of different financial time series. We show that this
approach is robust and powerful in detecting different types of multiscaling.
We observe a puzzling phenomenon where an apparent increase in multifractality
is measured in time series generated fro...

Triangulations of complex surfaces with different genera are studied within a statistical mechanics framework where an energy is associated to deviations from an ideal, ordered ground state. We observe that the complexity of the embedding surface strongly affects the properties of the triangulations. At high temperatures the ‘random states’ have de...

Minimum spanning trees and planar maximally filtered graphs are generated from correlations between the 300 most-capitalized NYSE stocks' daily returns, computed dynamically over moving windows of sizes between 1 and 12 months, in the period from 2001 to 2003. We study how different economic sectors differently populate the various regions of these...

We construct a partial order relation which acts on the set of 3-cliques of a maximal planar graph GG and defines a unique hierarchy. We demonstrate that GG is the union of a set of special subgraphs, named ‘bubbles’, that are themselves maximal planar graphs. The graph GG is retrieved by connecting these bubbles in a tree structure where neighbori...

We investigate the use of the Hurst exponent, dynamically computed over a
moving time-window, to evaluate the level of stability/instability of financial
firms. Financial firms bailed-out as a consequence of the 2007-2010 credit
crisis show a neat increase with time of the generalized Hurst exponent in the
period preceding the unfolding of the cris...

The statistical signatures of the 'credit crunch' financial crisis that unfolded between 2008 and 2009 are investigated by combining tools from statistical physics and network theory. We devise measures for the collective behavior of stock prices based on the construction of topologically constrained graphs from cross-correlation matrices. We test...

This Chapter is an introduction to the basic concepts used in complex systems studies. Our aim is to illustrate some fundamental ideas and provide a navigation map through some of the cutting edge topics in this emerging science. In particular, we will focus our attention to econophysics which mainly concerns the application of tools from statistic...

We introduce and describe in detail a "virtual laboratory" platform to study granular materials by combining advanced image reconstruction techniques from computed X-ray micro tomography and discrete element method simulations. This platform allows us to directly access quantities such as forces at the grain contacts, which would be otherwise hard...

It has been recently pointed out that local volume fluctuations in granular
packings follow remarkably well a shifted and rescaled Gamma distribution named
the kGamma distribution [T. Aste, T. Di Matteo, Phys. Rev. E 77 (2008) 021309].
In this paper we confirm, extend and discuss this finding by supporting it with
additional experimental and simula...

Two kinds of filtered networks: minimum spanning trees (MSTs) and planar maximally filtered graphs (PMFGs) are constructed from dynamical correlations computed over a moving window.
We study the evolution over time of both hierarchical and topological properties of these graphs in relation to market fluctuations.
We verify that the dynamical PMFG p...

We combine X-ray Computed Tomography data from real experimental samples with Discrete Element Method simulations to investigate the limiting packing fraction for the loosest mechanically-stable disordered packing. We establish a possible lower bound at packing fraction ∼53%.

In previous studies we have analyzed dynamical filtered graphs (namely the Minimum Spanning Trees and Planar Maximally Filtered Graphs) constructed from correlation matrices of daily return time series for the 300 most capitalized stocks of the New York Stock Exchange, and we have introduced centrality/peripherality synthetic indices which allowed...