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Pappada', Roberta (2014) Copula-based measures of tail dependence with applications. [Tesi di dottorato]

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Abstract (inglese)

With the advent of globalization and the recent financial turmoil, the interest for the analysis of dependencies between financial time series has significantly increased. Risk measures such as value-at-risk are heavily affected by the joint extreme comovements of associated risk factors. This thesis suggests some copula-based statistical tools which can be useful in order to have more insights into the nature of the association between random variables in the tail of their distributions.
Preliminarily, an overview of important definitions and properties in copula theory is given, and some known measures of tail dependence based on the notion of tail dependence coefficients and rank correlations are introduced. A first proposal consists of a graphical tool based on the so-called tail concentration function, in order to distinguish different families of copulas in a 2D configuration.
This can be used as a copula selection tool in practical fitting problems, when one wants to choose one or more copulas to model the dependence structure in the data, highlighting the information contained in the tail.
The thesis mainly deals with financial time series applications, where copula functions and the related concepts of tail copula and tail dependence coefficients are used to characterize the dependence structure of asset returns.
Classical cluster analysis tools are revisited by introducing suitable copula-based tail dependence measures, which are exploited in the identification of similarities or dissimilarities between the variables of interest and, in particular, between financial time series. Such an approach is designed to investigate the joint behaviour of pairs of time series when they are taking on extremely low values. Either the asymptotic and the finite behaviour are assessed. The proposed methodology is based on a suitable copula-based time series model(GARCH-copula model), in order to model the marginal behaviour of each time series separately from the dependence pattern. Moreover, non-parametric estimation procedures are adopted for describing the pairwise dependencies, thus avoiding any model assumption. Simulation studies are conducted in order to check the performances of the proposed procedures and applications to financial data are presented showing their practical implementation. The information coming from the output of the introduced clustering techniques can be exploited for automatic portfolio selection procedures in order to hedge the risk of a portfolio, by taking into account the occurrence of joint losses.
A two-stage portfolio diversification strategy is proposed and empirical analysis are provided. Results show how the suggested approach to the clustering of financial time series can be used by an investor to have more insights into the relationships among different assets in crisis periods. Moreover, the application to portfolio selection framework suggests a cautious usage of standard procedures that may not work when the markets are expected to experience periods of high volatility.

Abstract (italiano)

Con l'avvento della globalizzazione e la recente crisi finanziaria, l'interesse verso l'analisi delle relazioni tra serie storiche finanziarie è notevolmente aumentato. Misure di rischio come il value-at-risk sono fortemente influenzate dai movimenti estremi congiunti dei fattori di rischio associati.
Nella presente tesi si suggeriscono alcuni strumenti statistici basati sulla nozione di copula, che possono essere utili al fine di ottenere informazioni sulla natura dell'associazione tra variabili casuali nella coda delle loro distribuzioni.
Preliminarmente, vengono introdotte definizioni e proprietà fondamentali della teoria delle copule, e discusse alcune note misure di dipendenza basate sul concetto di coefficienti di dipendenza nella coda e correlazioni fra i ranghi. Una prima proposta consiste in uno strumento grafico basato sulla cosiddetta funzione di concentrazione di coda per distinguere tra diverse famiglie di copule in una configurazione bidimensionale. Questo strumento può essere impiegato in problemi pratici, quando si vuole scegliere tra una o più copule per modellizzare la struttura di dipendenza nei dati, evidenziando le informazioni contenute nella coda.
La tesi prende in considerazione diverse applicazioni nell'analisi di serie storiche finanziarie, in cui le funzioni copula e i relativi concetti di copule di coda e coefficienti di dipendenza nelle code vengono impiegati per caratterizzare la struttura di dipendenza dei rendimenti finanziari.
Gli strumenti standard per l'Analisi dei Gruppi (Cluster Analysis) vengono rivisitati attraverso l'introduzione di opportune misure di dipendenza, che permettano di identificare similarità o dissimilarità tra le quantità di interesse, nello specifico rappresentate da serie finanziarie. Tale approccio ha lo scopo di studiare il comportamento congiunto di coppie di serie finanziarie nel momento in cui esse assumono valori estremamente bassi. Vengono valutate sia la dipendenza asintotica che il comportamento finito. La metodologia proposta utilizza un modello per serie storiche basato sulle copule (GARCH-copula model), che consente di modellizzare il comportamento marginale di ogni serie temporale separatamente dalla struttura di dipendenza. Inoltre, vengono adottate procedure di stima non parametriche in relazione alla struttura di dipendenza, evitando così qualunque assunzione sul modello. Vengono condotti degli studi di simulazione per testare le procedure proposte e diverse applicazioni a dati finanziari mostrano la loro implementazione pratica.
Il risultato delle tecniche introdotte precedentemente può essere utilizzato in procedure di selezione automatica di portafoglio al fine di coprire il rischio dovuto al verificarsi di perdite congiunte. Viene proposta una strategia di diversificazione di portafoglio in due fasi e illustrate le analisi empiriche.
L'approccio suggerito per il raggruppamento di serie finanziarie può essere utile ad un investitore per avere una visione più approfondita delle correlazioni tra mercati finanziari in periodi di crisi. Inoltre, l'applicazione nell’ambito della selezione di portafogli suggerisce un uso prudente delle procedure standard che potrebbero non essere appropriate quando si prevede che i mercati possano attraversare periodi di alta volatilità.

Statistiche Download - Aggiungi a RefWorks
Tipo di EPrint:Tesi di dottorato
Relatore:Torelli, Nicola
Correlatore:Durante, Fabrizio
Dottorato (corsi e scuole):Ciclo 26 > Scuole 26 > SCIENZE STATISTICHE
Data di deposito della tesi:29 Gennaio 2014
Anno di Pubblicazione:29 Gennaio 2014
Parole chiave (italiano / inglese):Tail dependence, Copula, financial time series, Cluster Analysis
Settori scientifico-disciplinari MIUR:Area 13 - Scienze economiche e statistiche > SECS-S/01 Statistica
Struttura di riferimento:Dipartimenti > Dipartimento di Scienze Statistiche
Codice ID:6579
Depositato il:28 Apr 2015 17:55
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