Paper: arXiv 2405.11444

Abstract

A novel high-frequency market-making approach in discrete time is proposed that admits closed-form solutions. By taking advantage of demand functions that are linear in the quoted bid and ask spreads with random coefficients, we model the variability of the partial filling of limit orders posted in a limit order book (LOB). As a result, we uncover new patterns as to how the demand’s randomness affects the optimal placement strategy. We also allow the price process to follow general dynamics without any Brownian or martingale assumption as is commonly adopted in the literature. The most important feature of our optimal placement strategy is that it can react or adapt to the behavior of market orders online. Using LOB data, we train our model and reproduce the anticipated final profit and loss of the optimal strategy on a given testing date using the actual flow of orders in the LOB. Our adaptive optimal strategies outperform the non-adaptive strategy and those that quote limit orders at a fixed distance from the midprice.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces complex stochastic demand functions and general price dynamics without martingale assumptions, requiring advanced mathematical modeling; it is heavily data-driven, using LOB data for model training, calibration, backtesting, and out-of-sample validation across a year-long dataset.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Design adaptive market-making strategies<br>with closed-form solutions for LOB"] --> B{"Methodology"}
  
  B --> C["Model LOB Dynamics"]
  B --> D["Estimate Demand Functions<br>Linear in spreads with random coefficients"]
  B --> E["Derive Optimal<br>Placement Strategy"]
  
  C --> F["Data Processing<br>LOB training data"]
  D --> F
  E --> F
  
  F --> G["Computation"]
  
  G --> H["Train Model<br>Parameter estimation"]
  G --> I["Simulate Strategy<br>Apply to test date"]
  
  H --> J["Key Findings<br>• Adaptive strategy outperforms fixed/ non-adaptive<br>• Closed-form solutions enable online adaptation<br>• Captures impact of demand randomness"]