Hedging of volatility and correlation risk in a portfolio.

Summary This work focuses on the modeling of the dynamics of volatilities and correlations between financial assets returns. After a presentation of the literature on univariate and multivariate Garch models, the author establishes existence and uniqueness results for stationary solutions of dynamic correlation models of the DCC type (Engle, 2002). He then extends this class of models by including instantaneous volatilities and regime-switching probabilities in the dynamics of correlations. The new models are empirically evaluated on a portfolio of MSCI indices. Formal tests show that some of these new specifications improve the predictive power of the covariance matrix of returns and would be useful in portfolio management. Finally, focusing now on volatility risk, the author shows that hedging strategies of the main European equity indices based on implied volatility indices (VIX, VSTOXX) are relevant and allow both to hedge and reduce the equity risk of a portfolio.