Estimation of Multivariate Asset Models with Jumps

Angela Loregian, Laura Ballotta, Gianluca Fusai, and M. Fabricio Perez

We propose a consistent and computationally efficient 2-step methodology for the estimation of multidimensional non-Gaussian asset models built using Lévy processes. The proposed framework allows for dependence between assets and different tail-behaviors and jump structures for each asset. Our procedure can be applied to portfolios with a large number of assets as it is immune to estimation dimensionality problems. Simulations show good finite sample properties and significant efficiency gains. This method is especially relevant for risk management purposes such as, for example, the computation of portfolio Value at Risk and intra-horizon Value at Risk, as we show in detail in an empirical illustration.