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We introduce a copula-based dynamic model for multivariate processes of (non-negative) high-frequency trading variables revealing time-varying conditional variances and correlations. Modeling the variables’ conditional mean processes using a multiplicative error model we map the resulting residuals into a Gaussian domain using a Gaussian copula. Based on high-frequency volatility, cumulative trading volumes, trade counts and market depth of various stocks traded at the NYSE, we show that the proposed copula-based transformation is supported by the data and allows capturing (multivariate) dynamics in higher order moments. The latter are modeled using a DCC-GARCH specification. We suggest estimating the model by composite maximum likelihood which is sufficiently flexible to be applicable in high dimensions. Strong empirical evidence for time-varying conditional (co-)variances in trading processes supports the usefulness of the approach. Taking these higher-order dynamics explicitly into account significantly improves the goodness-of-fit of the multiplicative error model and allows capturing time-varying liquidity risks.
Euro area data show a positive connection between sovereign and bank risk, which increases with banks’ and sovereign long run fragility. We build a macro model with banks subject to incentive problems and liquidity risk (in the form of liquidity based banks’ runs) which provides a link between endogenous bank capital and macro and policy risk. Our banks also invest in risky government bonds used as capital buffer to self-insure against liquidity risk. The model can replicate the positive connection between sovereign and bank risk observed in the data. Central bank liquidity policy, through full allotment policy, is successful in stabilizing the spiraling feedback loops between bank and sovereign risk.