Giovanni De Luca

Mixture Processes for Financial Intradaily Durations

The instantaneous volatility of the price process is analyzed through the intraday financial durations between price changes. Previous research has traditionally dealt with parametric models without reaching a satisfactory level of adequacy. In this study, it is shown that by using a mixture of two exponential distributions a highly satisfactory fit can be obtained. The presence on financial markets of traders with different information sets makes reasonable the mixture assumption.

A tail dependence-based dissimilarity measure for financial time series clustering

In this paper we propose a clustering procedure aimed at grouping time series with an association between extremely low values, measured by the lower tail dependence coefficient. Firstly, we estimate the coefficient using an Archimedean copula function. Then, we propose a dissimilarity measure based on tail dependence coefficients and a two-step procedure to be used with clustering algorithms which require that the objects we want to cluster have a geometric interpretation. We show how the results of the clustering applied to financial returns could be used to construct defensive portfolios reducing the effect of a simultaneous financial crisis.

A multivariate skew-garch model

Empirical research on European stock markets has shown that they behave differently according to the performance of the leading financial market identified as the US market. A positive sign is viewed as good news in the international financial markets, a negative sign means, conversely, bad news. As a result, we assume that European stock market returns are affected by endogenous and exogenous shocks. The former raise in the market itself, the latter come from the US market, because of its most influential role in the world. Under standard assumptions, the distribution of the European market index returns conditionally on the sign of the one-day lagged US return is skew-normal. The resulting model is denoted Skew-GARCH. We study the properties of this new model and illustrate its application to time-series data from three European financial markets.

Time-Varying Mixing Weights in Mixture Autoregressive Conditional Duration Models

Financial market price formation and exchange activity can be investigated by means of ultra-high frequency data. In this article, we investigate an extension of the Autoregressive Conditional Duration (ACD) model of Engle and Russell (1998) by adopting a mixture of distribution approach with time-varying weights. Empirical estimation of the Mixture ACD model shows that the limitations of the standard base model and its inadequacy of modelling the behavior in the tail of the distribution are suitably solved by our model. When the weights are made dependent on some market activity data, the model lends itself to some structural interpretation related to price formation and information diffusion in the market.

Regime-switching Pareto distributions for ACD models

Refinements have been proposed for the autoregressive conditional duration model within the framework of financial durations. It is argued that a Pareto distribution is a meaningful representation for durations. The model is analyzed under the hypothesis of regime-switching parameters with different transition functions governed both by an observable and a latent variable.

Multivariate Tail Dependence Coefficients for Archimedean Copulae

We analyze the multivariate upper and lower tail dependence coefficients, obtained extending the existing definitions in the bivariate case. We provide their expressions for a popular class of copula functions, the Archimedean one. Finally, we apply the formulae to some well known copula functions used in many financial analyses.

Modelling multivariate skewness in financial returns: a SGARCH approach

Skewness of financial time series is a relevant topic, due to its implications for portfolio theory and for statistical inference. In the univariate case, its default measure is the third cumulant of the standardized random variable. It can be generalized to the third multivariate cumulant that is a matrix containing all centered moments of order three which can be obtained from a random vector. The present paper examines some properties of the third cumulant under the assumptions of the multivariate SGARCH model introduced by De Luca, Genton, and Loperfido [2006. A multivariate skew-GARCH model. Advances in Econometrics 20: 33–57]. In the first place, it allows for parsimonious modelling of multivariate skewness. In the second place, all its elements are either null or negative, consistently with previous empirical and theoretical findings. A numerical example with financial returns of France, Spain and Netherlands illustrates the theoretical results in the paper.

Archimedean copulae for risk measurement

In this paper some Archimedean copula functions for bivariate financial returns are studied. The choice of this family is due to their ability to capture the tail dependence, which is an association measure we can detect in many bivariate financial time-series. A time-varying version of these copulae is also investigated. Finally, the Value-at-Risk is computed and its performance is compared across different copula specifications.

Time Series Clustering on Lower Tail Dependence for Portfolio Selection

In this paper we analyse a case study based on the procedure introduced by De Luca and Zuccolotto [8], whose aim is to cluster time series of financial returns in groups being homogeneous in the sense that their joint bivariate distributions exhibit high association in the lower tail. The dissimilarity measure used for such clustering is based on tail dependence coefficients estimated using copula functions. We carry out the clustering using an algorithm requiring a preliminary transformation of the dissimilarity index into a distance metric by means of a geometric representation of the time series, obtained with Multidimensional Scaling. We show that the results of the clustering can be used for a portfolio selection purpose, when the goal is to protect investments from the effects of a financial crisis.

A Copula-Based Quantile Model

A copula-based quantile model is built. The estimates are compared to the estimates obtained using the multivariate CAViaR model, which extends the univariate version of the model. The comparison is firstly made in terms of Kupiec and Christoffersen test. Moreover, a further comparison is made using two loss functions that evaluate the distances between the losses and the VaR measures in presence of a violation. The results show that the copula approach is highly competitive providing, in particular, estimated quantiles which generally imply a lower value for the two loss functions.