1,721,285 research outputs found
Evaluating value-at-risk measures in the presence of long memory conditional volatility
No full textWe compare the value-at-risk (VaR) bounds obtained from several models fitted to simulated long memory conditional variance processes. We show that most VaR comparison tests and loss functions may lead to the choice of a misspecified model that produces incorrect risk conditional coverage. The only, exception is the test proposed by Christoffersen et al (2001). However, with an opportunity cost loss function, we show that most models satisfy, the Basel accord requirements and that the cost of selecting a misspecified model is limited. Therefore, simple models are harmless approximations for the computation of the VaR, both under the users and regulators points of vie
Equity and CDS sector indices: Dynamic models and risk hedging
Full text linkThe recent financial crisis had a substantial impact on equity and
bond markets, as well as on the performances of managed portfolios which have been hit by the decrease of both indices. Nevertheless, the availability of indices monitoring the equity market volatility, the VIX index, credit markets default risk, and CDS indices, allows for the construction of hedging strategies. In this paper, we take the point of view of an equity investor who wants to hedge the equity risk by taking positions either on the VIX index or on CDS indices. In deriving the hedge ratios, we consider the joint dynamic of variables taking into account mean relations, variance spillovers, and asymmetry, as well as correlation changes over time. Our analysis is based on sectorial indices and shows the advantages of hedging and the impact of a model specification
Identification of Long memory in GARCH models
No full textAbstract: This work extends the analysis of Baillie, Bollerslev and
Mikkelsen (1996) and Bollerslev and Mikkelsen (1996) on the estimation and identification problems of the Fractionally Integrated Generalized Autoregressive Conditional Heteroskedastik (FIGARCH) model.We assess the power of different information criteria and tests in identifying the presence of long memory in the conditional variances. The analysis is performed with a Montecarlo simulation study. In detail, the focus on the Akaike, Hannan-Quinn, Shibata and Schwarz information criteria and on the Jarque-Bera test for normality, Box-Pierce test for residual correlation and Engle test for ARCH effects. This study verifies that information criteria clearly distinguish the presence of long memory while tests do not evidence any difference between the fitted long and short memory models. An empirical application is provided; it analyses, on a high frequency dataset, the returns of the FIB30, the future on the MIB30, the Italian stock market index of highly capitalized firms
Statistical Analysis of Financial Data: With Examples In R Gentle James Chapman and Hall/CRC Press, 646 pp, ISBN: 9781138599499
No full textVariance (Non) Causality in Multivariate GARCH
No full textThis paper extends the current literature on the variance-causality topic providing the coefficient restrictions ensuring variance noncausality within multivariate GARCH models with in-mean effects. Furthermore, this paper presents a new multivariate model, the exponential causality GARCH. By the introduction of a multiplicative causality impact function, the variance causality effects becomes directly interpretable and can therefore be used to detect both the existence of causality and its direction; notably, the proposed model allows for increasing and decreasing variance effects. An empirical application evidences negative causality effects between returns and volume of an Italian stock market index future contract.Multivariate GARCH, Variance causality, Volatility,
The Value of Protecting Venice from the Acqua Alta Phenomenon under Different Local Sea Level Rises
No full textVenice (Italy) is built on several islands inside a lagoon. It undergoes a periodical flooding phenomenon, called "Acqua Alta" (AA). A system of mobile dams, called Mo.S.E., is urrently under construction to protect it. When needed, several floodgates will be lifted to separate the lagoon from the Adriatic sea. AA, whose length and height has been increasing in recent years, is a random phenomenon, corre
lated with local sea level rise (LSLR). Several possible LSLRs can be assumed as consequences of different global warming scenarios. We investigate here the cost-benefit of Mo.S.E. under di¤erent possible LSLRs. First, we simulate the future patterns of AA for the next 50 years under alternative LSLRs. Then, we calculate the benefit of Mo.S.E., converting each avoided AA episode into an economic value (avoided cost). We show that the bene ts are just at the level of the costs, when a low LSLR is assumed and increase with LSLR, provided that it does not reache a catastrophic (yet unpredictable) extreme level
The Value of Protecting Venice from the Acqua Alta Phenomenon under Different Local Sea Level Rises
Full text linkVenice (Italy) is built on several islands inside a lagoon. It undergoes a periodical �ooding phenomenon, called "Acqua Alta" (AA). A system of mobile dams, called Mo.S.E., is currently under construction to protect it. When needed, several fl�oodgates will be lifted to separate the lagoon from the Adriatic sea. AA, whose length and height has been increasing in recent years, is a random phenomenon, correlated with local sea level rise (LSLR). Several possible LSLRs can be assumed as consequences of different
global warming scenarios. We investigate here the cost-bene�t of Mo.S.E. under different possible LSLRs.
First, we simulate the future patterns of AA for the next 50 years under alternative LSLRs. Then, we calculate the bene�t of Mo.S.E., converting each avoided AA episode into an economic value (avoided cost). We show that the bene�ts are just at the level of the costs, when a low LSLR is assumed and increase with LSLR, provided that it does not reache a catastrophic (yet unpredictable) extreme level
The Value of Protecting Venice from the Acqua Alta Phenomenon under Different Local Sea Level Rises
No full text
Long memory conditional heteroskedasticity and second order causality
No full textIn questa tesi estendo la letteratura corrente riguardo ai modelli GARCH a memoria lunga.
Dapprima considero il problema della stazionarietà, evidenziando il motivo per il quale le
definizioni correnti sono inadeguate, ricavando inoltre le condizioni di stazionarietà utilizzando un recente teorema di Zaffaroni (2000). Mi sono poi concentrato sul problema della stima rilevando
l'inapplicabilità della dimostrazione di Lee ed Hansen (1991) sulla consistenza dello stimatore di
quasi massima verosimiglianza, risultato contrario a quanto sostenuto da Baillie, Bollerslev e
Mikkelsen (1996). Suggerisco quindi una strada alternativa, utilizzando un recente lavoro di
Jeantheau (1998), evidenziandone tuttavia i limiti. Di conseguenza ho verificato la consistenza e la
correttezza delle stime di quasi massima verosimiglianza all'interno di un esperimento Montecarlo,
il cui scopo principale era invece quello dello studio dell'identificazione della memoria lunga nelle varianze condizionali. Questo studio Montecarlo dimostra che i criteri di informazione individuano correttamente la memoria lunga, mentre i test di correlazione ed effetti ARCH sui residui sono in sostanza inutili.
Ho poi considerato l'analisi della previsione delle varianze, assumendo un generatore a memoria
lunga per le varianze condizionali. Ho derivato l'equazione del previsore della varianza, estendendo
in questo senso un lavoro di Baillie e Bollerslev (1991). In seguito ho affrontato il problema del
calcolo del Value-at-Risk quando utilizziamo un modello mal specificato per la varianza. L'analisi è
stata condotta all'interno della classe dei modelli GARCH utilizzando un approccio Montecarlo. Ho
studiato quindi gli effetti di un'errata specificazione quando i dati sono generati da un modello
FIGARCH e per il VaR si utilizzano modelli a memoria breve. Ho confrontato i diversi modelli per
il VaR tramite un gruppo di test e con un approccio basato su funzioni di perdita. Posso così
dimostrare che il modello correttamente specificato permette una migliore stima del VaR, un
risultato atteso a priori. Ho esteso quindi l'analisi considerando anche gli effetti dell'aggregazione sul comportamento a memoria lunga delle varianze e sul calcolo del VaR. Tramite un esperimento Montecarlo verifico che la memoria lunga è robusta al processo di aggregazione, tuttavia tale comportamento è influenzato anche dall'ampiezza della memoria stessa. Per quanto riguarda il
confronto delle misure VaR ottenute da dati aggregati e non aggregati, verifico che o dati aggregati
permettono si ottenere stime migliori.
Ho infine considerato un problema diverso, l'individuazione della causalità del secondo ordine (tra
varianze). Dopo il riesame della letteratura sul tema estendo dapprima le definizioni ed i requisiti
teorici per ottenere la non causalità in un modello generale del tipo VARMA-GARCH-M.
Considero poi le diverse specificazioni GARCH multivariate utilizzate in letteratura per la stima
della causalità del secondo ordine, ne evidenzio i punti deboli e suggerisco quindi un nuovo
modello GARCH bivariato il cui scopo è quello di individuare non solo la presenza di causalità del
secondo ordine ma anche la sua direzione. Il modello viene poi testa in un'applicazione pratica.
Presento dapprima tutte le analisi preliminari alla costruzione delle serie dei volumi e dei
rendimenti del FIB30, utilizzando un database fornito dalla Borsa Italiana. Sulle serie filtrate ho
applicato diversi modelli per la causalità tra varianze, incluso quello suggerito nel presente lavoro.
Ho ottenuto il risultato atteso, vale a dire l'importanza della direzione di causalità tra varianze.
In this dissertation I extend the current literature on long memory GARCH processes. I considered
at first the stationarity problem, showing why current definitions are inadequate and deriving
stationarity conditions using a recent theorem of Zaffaroni (2000). I focused then on the estimation
problem, pointing out the inapplicability of the well known Lee and Hansen (1991) proof of consistency of quasi maximum likelihood estimators, the opposite of the claims of Baillie,
Bollerslev and Mikkelsen (1996). Therefore, I suggested the application of a recent study of
Jeantheau (1998), showing the limits of this approach. I showed then consistency and umbiasedness
of the Quasi Maximum Likelihood estimators within a Montecarlo experiment whose primary purpose was the study of the identification of long memory in conditional variances. This Montecarlo study shows that information criteria correctly detect long memory, while tests on residual correlations and residual ARCH effects are useless.
I turn then to the analysis of variance forecasts when we assume a long memory DGP for the
conditional variances. I derive the equation of the variance forecaster extending a previous work of
Baillie and Bollerslev (1991). I consider then the problem of Value-at-Risk computation when we
misspecify the model for the variance. This analysis was done within the GARCH class of models
and in a Montecarlo framework. I studied the effects of misspecifications when the data are
generated by a FIGARCH process and we compute VaR with short memory specifications. I compared the different VaR models with a group of tests and with a loss function approach. I show that the correctly specified model allow for a finer VaR computation, as expected. I extended then the previous result considering also the effects of aggregation on the long memory behaviour of the
variances and on the VaR computation. I show with a Montecarlo experiment that long memory in
variance is robust to the aggregation process; however this behaviour is influenced by the memory
strength. Considering the comparison of VaR measure computed with aggregated and nonaggregated
data, I show that aggregated data are in general preferred.
Finally I considered a different problem, the detection of second order causality, which is among
variances. After a review of the current literature on this topic I extend the definitions and
theoretical requirements for non-causality in a general VARMA-GARCH-M model. I considered
then the different multivariate GARCH specifications used in the literature to detect second order
causality, showing their drawbacks and suggesting a new bivariate GARCH model whose purpose
is the detection of the causality existence and direction among variances. The suggested model is
then tested within an applied framework. I present all the analysis referred to the construction of the returns and volume series of the FIB30 market, using a transaction database supplied by the Borsa Italiana. On the filtered 5-minute series I applied then different models for causality among
variances, included the one I suggested, obtaining an expected results, the sign of causality matter
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