Limit order book (LOB) modeling and dynamics analysis

1. Parse the raw ITCH messages (using Python's `pandas` or `itchio`) to create an event-level dataframe. 2. Reconstruct the limit order book at each timestamp, calculating bid/ask spread, depth at top 5 levels, and order imbalance (bid_vol - ask_vol). 3. Calculate a 5-second forward price return. Correlate the contemporaneous order imbalance with this future return to validate a simple signal. 4. Produce a summary report with plots of spread, depth, and signal performance.

1. Build an event-driven backtest engine that processes LOB updates and trade messages chronologically. 2. Implement a market-making strategy that quotes a spread around a micro-price, adjusting quotes based on inventory skew and short-term volatility forecasts. 3. Model order fills probabilistically based on the strategy's queue position (e.g., using a Pro-Rata or FIFO fill model) rather than assuming instant fills. 4. Analyze P&L, inventory turnover, Sharpe ratio, and sensitivity to latency and queue priority assumptions.

1. Source and reconstruct the full depth-of-book data for the critical securities and correlated assets during the event window. 2. Quantify the collapse in depth, explosion in spread, and divergence in order flow toxicity (VPIN) metrics. 3. Model the feedback loop: how did aggressive selling trigger market-maker withdrawal, which in turn increased the price impact of subsequent orders? 4. Propose and simulate a set of robust risk controls or execution algorithms (e.g., dynamic participation rates, liquidity-seeking orders) that could have mitigated the crisis for a large institutional order.