Massimiliano Caporin

Flexible Dynamic Conditional Correlation multivariate GARCH models for asset allocation

This paper introduces the Flexible Dynamic Conditional Correlation (FDCC) multivariate GARCH model which generalizes the Dynamic Conditional Correlation (DCC) multivariate GARCH model proposed by Engle (2002). The FDCC model relax the assumption of common dynamics among all assets used in the DCC model. In fact, we cannot impose that the correlation dynamics of, say, European sectorial stock indexes are identical to the corresponding US ones. We thus extend the DCC model introducing a block-diagonal structure; in the FDCC the dynamics are constrained to be equal among groups of variables. We present an application to a sectorial asset allocation problem.

Measuring Sovereign Contagion in Europe

This paper analyzes the sovereign risk contagion using credit default swaps (CDS) and bond premiums for the major eurozone countries. By emphasizing several econometric approaches (nonlinear regression, quantile regression and Bayesian quantile regression with heteroskedasticity) we show that propagation of shocks in Europes CDS has been remarkably constant for the period 2008-2011 even though a significant part of the sample periphery countries have been extremely affected by their sovereign debt and fiscal situations. Thus, the integration among the different eurozone countries is stable, and the risk spillover among these countries is not affected by the size of the shock, implying that so far contagion has remained subdue. Results for the CDS sample are confirmed by examining bond spreads. However, the analysis of bond data shows that there is a change in the intensity of the propagation of shocks in the 2003-2006 pre-crisis period and the 2008-2011 post-Lehman one, but the coefficients actually go down, not up! All the increases in correlation we have witnessed over the last years come from larger shocks and the heteroskedasticity in the data, not from similar shocks propagated with higher intensity across Europe. This is the fi rst paper, to our knowledge, where a Bayesian quantile regression approach is used to measure contagion. This methodology is particularly well-suited to deal with nonlinear and unstable transmission mechanisms.

Multivariate Markov Switching Dynamic Conditional Correlation GARCH representations for contagion analysis

Abstract.This paper provides an extension of the Dynamic Conditional Correlation model of Engle (2002) by allowing both the unconditional correlation and the parameters to be driven by an unobservable Markov chain. We provide the estimation algorithm and perform an empirical analysis of the contagion phenomenon in which our model is compared to the traditional CCC and DCC representations.

Market linkages, variance spillovers, and correlation stability: Empirical evidence of financial contagion

To model the contemporaneous relationships among Asian and American stock markets, a simultaneous equation system with GARCH errors is introduced. In the estimated residuals, the correlation matrix is analyzed over rolling windows and using a correlation matrix distance, which allows a graphical analysis and the development of a statistical test of correlation movements. Furthermore, a methodology that can be used to identify turmoil periods on a data-driven basis is presented. The previous results are applied in the analysis of the contagion issue between Asian and American stock markets. The results show some evidence of contagion, and the proposed statistics identify, on a data-driven basis, turmoil periods consistent with the ones currently assumed in the literature.

A generalized Dynamic Conditional Correlation model for portfolio risk evaluation

We propose a generalization of the Dynamic Conditional Correlation multivariate GARCH model of Engle [R.F. Engle, Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models, Journal of Business and Economic Statistics 20 (2002) 339-350] and of the Asymmetric Dynamic Conditional Correlation model of Cappiello et al.[L. Cappiello, R.F. Engle, K. Sheppard, Asymmetric dynamics in the correlations of global equity and bond returns, Journal of Financial Econometrics 25 (2006) 537-572]. The model we propose introduces a block structure in parameter matrices that allows for interdependence with a reduced number of parameters. Our model nests the Flexible Dynamic Conditional Correlation model of Billio et al. [M. Billio, M. Caporin, M. Gobbo, Flexible dynamic conditional correlation multivariate GARCH for asset allocation, Applied Financial Economics Letters 2 (2006) 123-130] and is named Quadratic Flexible Dynamic Conditional Correlation Multivariate GARCH. In the paper, we provide conditions for positive definiteness of the conditional correlations. We also present an empirical application to the Italian stock market comparing alternative correlation models for portfolio risk evaluation.

Robust ranking of multivariate GARCH models by problem dimension

Several Multivariate GARCH (MGARCH) models have been proposed, and recently such MGARCH specifications have been examined in terms of their out-of-sample forecasting performance. An empirical comparison of alternative MGARCH models is provided, which focuses on the BEKK, DCC, Corrected DCC (cDCC), CCC, OGARCH models, Exponentially Weighted Moving Average, and covariance shrinking, all fitted to historical data for 89 US equities. Notably, a wide range of models, including the recent cDCC model and the covariance shrinking method, are used. Several tests and approaches for direct and indirect model comparison, including the Model Confidence Set, are considered. Furthermore, the robustness of model rankings to the cross-sectional dimension of the problem is analyzed.

A note on calculating autocovariances of long‐memory processes

In this paper, we consider a method (splitting) for calculating the autocovariances of fractional integrated processes (ARFIMA) and generalized integrated processes (GARMA). The splitting method does not require any restriction on the autoregressive roots, and allows fast calculation of the autocovariances of these processes.

Modelling and forecasting wind speed intensity for weather risk management

The main interest of the wind speed modelling is on the short-term forecast of wind speed intensity and direction. Recently, its relationship with electricity production by wind farms has been studied. In fact, electricity producers are interested in long-range forecasts and simulation of wind speed for two main reasons: to evaluate the profitability of building a wind farm in a given location, and to offset the risks associated with the variability of wind speed for an already operating wind farm. Three approaches that are capable of forecasting and simulating the long run evolution of wind speed intensity are compared (wind direction is not a concern, given that the recent turbines can rotate to follow wind direction). The evaluated models are: the Auto Regressive Gamma process, the Gamma Auto Regressive process, and the ARFIMA-FIGARCH model. Both in-sample and out-of-sample comparisons are provided, as well as some examples for the pricing of wind speed derivatives using a model-based Monte Carlo simulation approach.

Periodic Long-Memory GARCH Models

A distinguishing feature of the intraday time-varying volatility of financial time series is given by the presence of long-range dependence of periodic type, due mainly to time-of-the-day phenomena. In this work, we introduce a model able to describe the empirical evidence given by this periodic long-memory behaviour. The model, named PLM-GARCH (Periodic Long-Memory GARCH), represents a natural extension of the FIGARCH model proposed for modelling long-range persistence of volatility. Periodic long memory versions of EGARCH (PLM-EGARCH) and of Log-GARCH (PLM-LGARCH) models are also examined. Some properties and characteristics of the models are given and finite sample performance of quasi-maximum likelihood estimation are studied with Monte Carlo simulations. Further possible extensions of the model to take into account multiple sources of periodic long-memory behaviour are proposed. Two empirical applications on intra-day financial time series are also provided.

Generalised long-memory GARCH models for intra-daily volatility

The class of fractionally integrated generalised autoregressive conditional heteroskedastic (FIGARCH) models is extended for modelling the periodic long-range dependence typically shown by volatility of most intra-daily financial returns. The proposed class of models introduces generalised periodic long-memory filters, based on Gegenbauer polynomials, into the equation describing the time-varying volatility of standard GARCH models. A fitting procedure is illustrated and its performance is evaluated by means of Monte Carlo simulations. The effectiveness of these models in describing periodic long-memory volatility patterns is shown through an empirical application to the Euro-Dollar intra-daily exchange rate.