We find and describe four futures markets where the bid-ask spread is bid down to the fixed price tick size practically all the time, and which match counterparties using a pro-rata rule. These four markets' offered depths at the quotes on average exceed mean market order size by two orders of...

We examine moving average (MA) filters for estimating the integrated variance (IV) of a financial asset price in a framework where high-frequency price data are contaminated with market microstructure noise. We show that the sum of squared MA residuals must be scaled to enable a suitable...

Financial assets' quoted prices normally change through frequent revisions, or jumps. For markets where quotes are almost always revised by the minimum price tick, this paper proposes a new estimator of Quadratic Variation which is robust to microstructure effects. It compares the number of...

This paper models limit order books where each trader is uncertain of the underlying distribution in the asset's value to others. If this uncertainty is rapidly resolved, fleeting limit orders are submitted and quickly cancelled. This enhances liquidity supply, but leaves intact established...

For financial assets whose best quotes almost always change by jumping by the market's price tick size (one cent, five cents, etc.), this paper proposes an estimator of Quadratic Variation which controls for microstructure effects. It measures the prevalence of alternations, where quotes jump...

Financial assets` quoted prices normally change through frequent revisions, or jumps. For markets where quotes are almost always revised by the minimum price tick, this paper proposes a new estimator of Quadratic Variation which is robust to microstructure effects. It compares the number of...

This paper models limit order books where each trader is uncertain of the underlying distribution in the asset`s value to others. If this uncertainty is rapidly resolved, fleeting limit orders are submitted and quickly cancelled. This enhances liquidity supply, but leaves intact established...

Using a stochastic sequential game in ergodic equilibrium, this paper models limit order book trading dynamics. It deduces investor surplus and some agents` strategies from depth`s stationarity, while bypassing altogether agents` intricate forecasting problems. Market inefficiency adjusts to...

Limit order markets with stationary dynamics attract equal volumes of market orders and uncanceled limit orders, equalizing the supply and demand for liquidity and immediacy. To maintain this balance, market orders must share any benefit obtained by limit order traders from more efficient...