Riemannian-geometric regime-switching covariance hedging

This study develops a regime-switching Riemannian-geometric covariance framework for futures hedging. The covariance of conventional regime-switching BEKK (Baba, Engle, Kraft and Kroner) (RSBEKK) evolves on flat spaces that exclude a prior the possibility of inherent geometric covariance dynamic. A Riemannian-geometric regime-switching BEKK (RG-RSBEKK) is proposed such that the covariance moves along a trajectory on Riemannian manifolds. RG-RSBEKK is applied to China Securities Index 300 futures for hedging the stock sector exposures. Empirical results reveal that specifying covariance dynamic on curved spaces enhances hedging effectiveness based on the model confidence set with loss measures of variance, utility, value-at-risk, and Frobenius distance.