Multivariate multifractal models: estimation of parameters and applications to risk management
In this thesis, we have reviewed fractal and multi-fractal concepts from natural science, as well as their implications in financial economics. The main contribution of this thesis is the development of bivariate multi-fractal model extending the univariate Markov-switching multi-fractal model. We have implemented its estimation via different approaches, including GMM, maximum likelihood and particle filter approaches. To reveal the applicability of our multivariate MF model, two well-known instruments in financial risk management, namely Value-at-Risk and Expected Shortfall have been used for the model assessment.