Copula based multivariate semi-Markov models with applications in high-frequency finance

We introduce a new multivariate model of multiple asset returns. Our model is based on weighted in- dexed semi-Markov chains to describe the single (marginals) asset returns, whereas the dependence structure among the considered assets is described by introducing copula functions. A real application of the proposed multivariate model is presented based on the evolution of 6 stocks from the Italian Stock Exchange. We provide empirical evidence that the model is able to correctly reproduce statistical regular- ities of multivariate real data such as the cross-correlation function, value-at-risk, marginal value-at-risk and conditional value-at-risk. The model is also used for volatility forecasting of each stock.