When large trades are not (automatically) news: liquidity tail risk and price discovery

Battle Count: 79

Highly relevant to quantitative trading. The paper provides a rigorous theoretical framework for understanding how heavy-tailed liquidity demand affects price impact, bid-ask spreads, and information revelation in limit order books. Key practical implications include: (1) large trades should not be automatically interpreted as informed when liquidity tails are heavy, affecting signal extraction in algorithmic trading; (2) the crossover-depth concept informs optimal order sizing and execution timing; (3) persistent spreads after large heavy-tailed trades affect transaction cost models; (4) the tail exponent predictions provide testable hypotheses for market impact models; (5) the empirical findings on AAPL, MSFT, and INTC provide direct evidence for practitioners on how tail-risk regimes affect price discovery and liquidity. The model's predictions about flatter price impact and slower learning under heavy tails are directly actionable for execution algorithms and market-making strategies.

Very high implementation complexity. The theoretical framework involves: (1) solving a non-linear fixed-point equation for the marginal-cost schedule on a tail-controlled compact class; (2) implementing Bayesian posterior updates with dependent data under Student-t likelihood; (3) computing regular variation exponents recursively across trading periods; (4) handling the failure of standard monotonicity and compactness arguments. The numerical implementation requires careful grid construction, iterative fixed-point solving with convergence monitoring, convolution computations with Student-t kernels, and posterior updates. The empirical component requires Hill estimator implementation, Newey-West HAC regression, and careful data preprocessing of LOBSTER message files. The mathematical sophistication (regular variation theory, Schauder fixed-point theorem, Girsanov theorem, martingale convergence) makes this primarily a research-level contribution rather than a directly implementable trading system.

The paper provides detailed numerical setup (grid specifications, tolerance thresholds, parameter choices) and uses publicly available LOBSTER data for AAPL, MSFT, and INTC. However, the theoretical proofs are complex and the numerical implementation details, while described, would require significant effort to replicate. The empirical analysis uses standard econometric methods (Hill estimator, OLS with Newey-West corrections) that are well-documented. No code repository is mentioned.