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Title: A general framework for multifractal discrete stochastic volatility Authors:  Arnaud Dufays - EDHEC Business school (France) [presenting]
Maciej Augustyniak - University of Montreal (Canada)
Kassimou Abdoul Haki Maoude - University of Montreal (Canada)
Abstract: Regime-switching processes are popular tools to interpret, model and forecast financial data. The Markov-switching multifractal (MSM) model has proved to be a strong competitor to the GARCH class of models for modeling the volatility of returns. In this model, volatility dynamics are driven by a latent high-dimensional Markov chain constructed by multiplying independent two-state Markov chains. We propose the multifractal discrete stochastic volatility (MDSV) model as a generalization of the MSM process and of other related high-dimensional hidden Markov models. Our model is intended to model financial returns jointly and realized volatilities, and therefore also extends existing high-dimensional Markov-switching processes to the joint setting. Our approach consists in building a high-dimensional Markov chain by the product of lower-dimensional Markov-chains which have a discrete stochastic volatility representation. The properties and structure of our model are studied theoretically, and it is shown that the MDSV process can be interpreted as a multi-component stochastic volatility model. An empirical study on 31 financial time series shows that the MDSV model can improve upon the realized EGARCH model in terms of fit and forecasting performance.