Liquidity Jump, Liquidity Diffusion, and Portfolio of Assets with Extreme Liquidity

We model a portfolio of crypto assets that does not respond well to multivariate autoregressive models because of discontinuity in conditional covariance matrix and posterior covariance matrix caused by extreme liquidity. We adjust asset-level return and volatility with liquidity to reduce such discontinuity, and restore the effectiveness of a set of liquidity-adjusted VECM-DCC/ADCC-BL models at extreme liquidity. We establish two distinctive yet complementary portfolio liquidity measures: portfolio liquidity jump that quantifies the effect of liquidity adjustment in forecasting the conditional covariance matrix, and portfolio liquidity diffusion that quantifies the effect of liquidity adjustment in estimating the posterior covariance matrix.