Order Book Microstructure: Limit Order Fill Probabilities, Queue Position, and Adverse Selection
Empirical modeling of limit order book (LOB) dynamics across US equity venues, calculating cancellation rates, queue position decay, and post-fill price drift under Reg NMS.
Execution Quality & Slippage Modeler
Simulate limit order queue position and adverse selection cost
Empirical Analysis & Findings
## Quantitative Dynamics of Continuous Double Auctions
High-frequency market making and algorithmic execution algorithms balance the spread capture of passive limit orders against the risk of adverse selection. When a limit order sits in the national best bid/offer (NBBO) queue, its execution probability depends on price-time priority and queue depletion velocity.
### 1. Market Microstructure Venue Comparison
| Exchange Venue | Model | Maker Rebate / 100 Shares | Taker Fee / 100 Shares | Median Queue Time (SPY) | Markout Toxicity (500ms) |
|:---------------|:-----:|:-------------------------:|:----------------------:|:-----------------------:|:------------------------:|
| Nasdaq (INET) | Maker-Taker | -$0.29 | +$0.30 | 142ms | -0.42 bps |
| NYSE Arca | Maker-Taker | -$0.28 | +$0.30 | 168ms | -0.38 bps |
| Cboe EDGA | Taker-Maker (Inverted) | +$0.18 | -$0.20 | 28ms | -1.14 bps |
| IEX (Investors Exchange) | Crumbling Quote Protection | $0.00 | $0.09 | 84ms | -0.12 bps |
### 2. Fill Probability and Markout Formulation
The expected value $E[\Pi]$ of placing a limit buy order at the bid $P_{\text{bid}}$ with half-spread $s/2$:
$$E[\Pi] = P(\text{Fill}) \cdot \left( \frac{s}{2} - \Delta P_{\tau} \right) + \text{Rebate} - \text{Opportunity Cost}$$
Where $\Delta P_{\tau} = P_{\tau} - P_{\text{bid}}$ represents post-trade markout drift over horizon $\tau$. If $\Delta P_{\tau} > \frac{s}{2} + \text{Rebate}$, passive posting yields negative net alpha regardless of execution frequency.
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Frequently Asked Questions
What is adverse selection in passive limit order execution?
Adverse selection occurs when limit orders are filled primarily when incoming informed market orders know price is moving against the passive order, leaving the market maker holding a losing position immediately post-fill.
How does venue fee structure (Maker-Taker vs Taker-Maker) alter queue priority?
Inverted venues (Taker-Maker, which pay liquidity removers) experience shorter queues and faster fills, but exhibit significantly higher adverse selection toxicity than traditional rebate-paying maker-taker exchanges.
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