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SESSION I-2 : FINANCIAL MODELING (18/12/2008 à 09h00)

Contemporaneous Aggregation of GARCH Models and Evaluation of the Aggregation Bias

Auteurs : JONDEAU Eric (Swiss Finance Institute and University of Lausanne)

Intervenants : JONDEAU Eric (Swiss Finance Institute and University of Lausanne)

It is well known that the class of strong (Generalized) AutoRegressive Conditional Heteroskedasticity (or GARCH) processes is not closed under contemporaneous aggregation. This paper provides the dynamics followed by the aggregate process when the individual persistence parameters are drawn from the same (unknown) distribution. Assuming heterogeneity across individual parameters, the dynamics of the aggregate volatility involves additional lags that reflect the moments of the distribution of the individual persistence parameters. Then the paper describes a consistent estimator of the aggregate process, based on nonlinear least squares. A simulation study reveals that this aggregation-corrected estimator performs very well under realistic sets of parameters. Last, this approach is extended to a multi-sector context. This extension is used to evaluate the importance of the aggregation bias. Using size and book-to-market portfolios, I show that the investor is willing to pay one fifth of her expected return to switch from the standard GARCH(1,1) estimator to the aggregation-corrected estimator.

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Hierarchical Hidden Markov Structure for Dynamic Correlations: the Hierarchical RSDC Model

Auteurs : CHARLOT Philippe (GREQAM & Université de la Méditerranée); Vêlayoudom MARIMOUTOU (GREQAM, Aix Marseille University & IFP)

Intervenants : CHARLOT Philippe (GREQAM & Université de la Méditerranée)

This paper presents a new multivariate GARCH model with time-varying conditional correlation structure which is a generalization of the Regime Switching Dynamic Correlation (RSDC) of Pelletier (2006). This model, which we name Hierarchical RSDC, is building with the hierarchical generalization of the hidden Markov model introduced by Fine et al. (1998). This can be viewed graphically as a tree-structure with different types of states. The first are called production states and they can emit observations, as in the classical Markov-Switching approach. The second are called abstract states. They can’t emit observations but establish vertical and horizontal probabilities that define the dynamic of the hidden hierarchical structure. The main gain of this approach compared to the classical Markov-Switching model is to increase the granularity of the regimes. Our model is also compared to the new Double Smooth Transition Conditional Correlation GARCH model (DSTCC), a STAR approach for dynamic correlations proposed by Silvennoinen and Teräsvirta (2007). The reason is that under certain assumptions, the DSTCC and our model represent two classical competing approaches to modelling regime switching. We also perform Monte-Carlo simulations and we apply the model to two empirical applications studying the conditional correlations of selected stock returns. Results show that the Hierarchical RSDC provides a good measure of the correlations and also has an interesting explanatory power.

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Contributions to The Estimation of Mixed-State Conditionally Heteroscedastic Latent Factor Models: A Comparative Study

Auteurs : SAIDANE Mohamed (The University of 7 November at Carthage); LAVERGNE Christian (University of Montpellier 2)

Intervenants : SAIDANE Mohamed (The University of 7 November at Carthage)

Mixed-State conditionally heteroscedastic latent factor models attempt to describe a complex nonlinear dynamic system with a succession of linear latent factor models indexed by a switching variable. Unfortunately, despite the framework's simplicity exact state and parameter estimation are still intractable because of the interdependency across the latent factor volatility processes. Recently, a broad class of learning and inference algorithms for time series models have been successfully cast in the framework of dynamic Bayesian networks (DBN). This paper describes a novel DBN-based switching conditionally heteroscedastic latent factor model. The key methodological contribution of this paper is the novel use of the Generalized Pseudo-Bayesian method GPB2, a structured variational learning approach and an approximated version of the Viterbi algorithm in conjunction with the EM algorithm for overcoming the intractability of exact inference in mixed-state latent factor model. The conditional EM algorithm that we have developed for the maximum likelihood estimation is based on an extended switching Kalman filter approach which yields inferences about the unobservable path of the common factors and their variances, and the latent variable of the state process. Extensive Monte Carlo simulations show promising results for tracking, interpolation, synthesis, and classification using learned models.

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