We develop a model of an order-driven exchange competing for order flow with off-exchange trading mechanisms. Liquidity suppliers face a trade-off between benefits and costs of order exposure. If they display trading intentions, they attract additional trade demand. We show, in equilibrium,...

We introduce a regularization and blocking estimator for well-conditioned high-dimensional daily covariances using high-frequency data. Using the Barndorff-Nielsen, Hansen, Lunde, and Shephard (2008a) kernel estimator, we estimate the covariance matrix block-wise and regularize it. A data-driven...

Estimation and forecasting for realistic continuous-time stochastic volatility models is hampered by the lack of closed-form expressions for the likelihood. In response, Andersen, Bollerslev, Diebold, and Labys ("Econometrica", 71 (2003), 579-625) advocate forecasting integrated volatility via...

In Andersen and Bondarenko (2014), using tick data for S&P 500 futures, we establish that the VPIN metric of Easley, Lopez de Prado, and O'Hara (ELO), by construction, will be correlated with trading volume and return volatility (innovations). Whether VPIN is more strongly correlated with volume...

We study the dynamic relation between market risks and risk premia using time series of index option surfaces. We find that priced left tail risk cannot be spanned by market volatility (and its components) and introduce a new tail factor. This tail factor has no incremental predictive power for...