Alpha-Skewed Optimal Market Making Engine

In market making, every parameter is a trade-off between Spread Capture and Adverse Selection. This project uses HJB control to find the mathematically optimal point on that frontier in real time.

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Project Showcase: Alpha-Skewed Optimal Market Making Engine (CT-LiT + HJB)

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  Continuous-Time LOB Transformer  x  Cartea-Jaimungal Stochastic Control

Inspiration

In electronic financial markets, high-frequency market makers provide the critical liquidity that allows participants to trade efficiently. By continuously quoting Limit Buy (Bid) and Limit Sell (Ask) orders, market makers aim to capture the fractional bid-ask spread across millions of daily transactions.

However, traditional market makers face an existential dilemma known as the Adverse Selection Paradox:

  1. The Toxic Sweep Problem: When informed institutional algorithms or momentum traders execute large aggressive market orders, they sweep through the book right before a major price jump or drop. Traditional symmetric market makers get filled on the wrong side of the market right before the crash, suffering immediate post-trade losses.
  2. The Martingale Flaw in Classical Models: Classical quantitative models, such as the seminal Avellaneda-Stoikov (2008) framework, assume that the asset's mid-price follows a pure driftless martingale ($dS_t = \sigma dW_t$). In reality, modern Level 2 (L2) order books contain rich, short-term predictive signals—order flow imbalances, queue micro-drifts, and asymmetric cancellation bursts. Blindly assuming zero drift causes market makers to build up toxic inventory during directional trend runs.

We were inspired to build a unified, institutional-grade quantitative trading system that bridges two cutting-edge domains:

  • Deep Learning Alpha Forecasting: Modeling continuous-time, asynchronous tick arrival patterns using Transformer architectures.
  • Stochastic Optimal Control (HJB): Solving the Cartea-Jaimungal drift-extended Hamilton-Jacobi-Bellman equation to dynamically skew quotes and mathematically dodge toxic sweeps.

What it does

The Alpha-Skewed Optimal Market Making Engine is an end-to-end, ultra-low-latency quantitative trading system designed for Level 2 Limit Order Book (L2 LOB) tick data.

[ L2 Raw Feeds ] ──► [ C++20 Order Book ] ──► [ Continuous Features ] ──► [ CT-LiT Alpha (α_t) ] ──► [ HJB Optimal Quoting ] ──► [ Execution Engine ]
 (Binance/CME)       (Zero-Alloc Top 20)       (OFI, MLI, Micro-Price)     (Time2Vec + Attention)     (Asymmetric Spreads)        (Queue Degradation)

Core Capabilities:

  1. Zero-Allocation L2 Order Book Reconstruction:
    • Maintains top-20 price levels for bids and asks in continuous flat static arrays with zero dynamic heap allocations (malloc/new).
    • Computes Micro-Price ($P_{\text{micro}}$), Cont & Kukanov (2014) Order Flow Imbalance (OFI), Multi-Level Imbalance ($MLI_1, MLI_5, MLI_{10}$), and EWMA rolling realized volatility in $\mathcal{O}(1)$ time.
  2. Continuous-Time Alpha Prediction (CT-LiT):
    • Encodes irregular, asynchronous nanosecond tick arrivals ($\Delta t$) using Time2Vec continuous sinusoidal embeddings.
    • Uses 1D convolutional depth patch projections and causal multi-head self-attention to forecast short-term directional price drift: $\hat{\alpha}t = \mathbb{E}[S{t+\Delta T} - S_t \mid \mathcal{F}_t]$.
  3. Stochastic Optimal Quoting & Reservation Pricing (HJB):
    • Solves the Cartea-Jaimungal drift-extended HJB equation in closed form to compute the analytical reservation price $r(s, q, t, \hat{\alpha})$ and asymmetric optimal bid/ask spreads $(\delta^b, \delta^a)$.
    • Automatically skews quotes: if bullish drift is detected, it tightens the bid quote to accumulate asset and widens the ask quote to avoid selling at stale prices; if bearish toxic flow is detected, it widens bids to dodge sweeps.
  4. Realistic Microstructure & Latency Matching Simulator:
    • Injects configurable wire latency ($25\,\mu\text{s}$).
    • Models probabilistic FIFO queue position degradation: $\Delta \text{QueuePos} = -\max(0, V_{\text{trades}} + \kappa_{\text{cancel}} V_{\text{cancels}})$.
    • Evaluates post-trade toxic adverse selection at 1ms and 5ms horizons.
  5. 4-Way PnL Attribution Suite:
    • Decomposes strategy returns: $\text{PnL}{\text{total}} = \text{PnL}{\text{spread}} + \text{PnL}{\text{alpha}} - \text{PnL}{\text{adverse_selection}} - \text{Fees}$.

How we built it

We built the repository from the ground up using a decoupled, dual-language architecture optimized for research flexibility and microsecond production execution:

lob-alpha-market-making/
├── core_engine/                 # Ultra-Low Latency C++20 Layer
│   ├── include/                 # Types, RingBuffer, OrderBook, QueueTracker, HJB, Risk, ONNX
│   └── src/                     # Zero-allocation implementations & microsecond simulator
├── ml_alpha/                    # PyTorch Continuous-Time Alpha Layer
│   ├── models/                  # Time2Vec, SpatialPatchProjector, CTLiTTransformer
│   ├── dataset/                 # Asynchronous tick dataset & non-overlapping sampler
│   └── training/                # Multi-objective loss (Huber + CE + Rank IC) & ONNX export
├── analytics/                   # Quantitative Backtest & Attribution Suite
│   ├── benchmark.py             # 3-way strategy backtest orchestrator
│   ├── metrics.py               # Annualized Sharpe, Sortino, Drawdown, Inventory Half-Life
│   ├── pnl_attribution.py       # 4-way PnL decomposition engine
│   └── plot_dashboard.py        # 4-panel visual reporting tear-sheet generator
└── tests/                       # Complete GoogleTest C++ & PyTest Python test suites

Key Technologies & Mathematical Implementation:

  • C++20 Hot Path:
    • Fixed-Point Arithmetic: Price ($10^{-8}$ scale factor 100,000,000LL) and Volume ($10^{-4}$ scale factor 10,000LL) eliminate IEEE 754 floating-point non-determinism.
    • Cache-Line Alignment: Core structures (MarketEvent, OrderBookLevel, Quote, Fill) use alignas(64) to fit 64-byte CPU cache lines and eliminate false sharing.
    • Lock-Free SPSC Ring Buffer: Non-blocking Single-Producer Single-Consumer queue with atomic memory barriers (std::memory_order_release/acquire).
  • PyTorch Deep Learning & ONNX Quantization:
    • Time2Vec Embedding: Decomposes continuous inter-arrival time $\tau = \Delta t$ into linear trends ($\omega_0 \tau + \phi_0$) and periodic burst harmonics ($\sin(\omega_i \tau + \phi_i)$).
    • Spatial Patch Projector: 1D Convolutions map 20 L2 depth levels into latent embeddings.
    • Causal Transformer Encoder: Multi-head self-attention with lower-triangular causal masks.
    • Multi-Objective Loss: $\mathcal{L} = w_1 \mathcal{L}{\text{Huber}} + w_2 \mathcal{L}{\text{CE}} + w_3 (1 - \rho_{\text{Rank}})$.
    • ONNX Export: Quantized graph export verified via onnx.checker and onnxruntime.
  • Stochastic Optimal Control Formulation:
    • Analytical Reservation Price: $$r(s, q, t, \hat{\alpha}) = s + \frac{\hat{\alpha}}{\gamma \sigma^2}\left(1 - e^{-\gamma \sigma^2 (T-t)}\right) - q \gamma \sigma^2 (T - t)$$
    • Optimal Asymmetric Quoting Spreads: $$\delta^b = \frac{1}{\kappa} \ln\left(1 + \frac{\kappa}{\gamma}\right) + \frac{(2q - 1)\gamma \sigma^2 (T-t)}{2} - \frac{\hat{\alpha}}{\kappa}$$ $$\delta^a = \frac{1}{\kappa} \ln\left(1 + \frac{\kappa}{\gamma}\right) - \frac{(2q + 1)\gamma \sigma^2 (T-t)}{2} + \frac{\hat{\alpha}}{\kappa}$$

Challenges we ran into

  1. Handling Continuous-Time Asynchrony in Neural Networks:
    • Problem: Traditional sequence models assume uniform discrete time intervals ($t=1,2,3$). In reality, 50 ticks can arrive in 2ms during a volatility cascade or over 10s in a quiet regime.
    • Solution: We implemented continuous-time positional embeddings via Time2Vec, allowing the attention heads to explicitly learn the continuous frequency spectrum of order arrivals.
  2. Eliminating Heap Allocations on the Matching Hot Path:
    • Problem: Standard C++ STL containers (std::vector, std::map, std::string) invoke heap allocations (malloc/free) and cause non-deterministic OS latency spikes.
    • Solution: Re-engineered the entire order book and queue tracker using fixed static contiguous memory arrays (std::array<OrderBookLevel, 20>), pre-allocated tensor sliding buffers with std::memmove, and lock-free circular queues.
  3. Mathematical Numerical Singularities in HJB Drift Scaling:
    • Problem: When risk aversion or remaining time horizon is small ($\gamma \sigma^2 \tau \to 0$), the drift adjustment factor $\frac{1 - e^{-\gamma \sigma^2 \tau}}{\gamma \sigma^2}$ produces numerical $0/0$ division instabilities.
    • Solution: Derived a stable Taylor series expansion: $\frac{1 - e^{-x}}{x} \approx 1 - \frac{x}{2} + \frac{x^2}{6}$ for $|x| < 10^{-5}$, guaranteeing floating-point and fixed-point numerical stability under all market regimes.
  4. Microstructure Queue Degradation vs. Immediate Fill Delusions:
    • Problem: Naive backtesters assume limit orders are filled the moment market price touches the quote price, producing artificially inflated Sharpe ratios.
    • Solution: Modeled realistic FIFO queue degradation tracking ahead-of-queue volume, proportional cancellation depletion, and wire latency delays.

Accomplishments that we're proud of

  • ⚡ Blistering Execution Speed: Achieved >14 million events/sec matching throughput ($<0.08\,\mu\text{s}$ or 72.5 nanoseconds per tick) on a single core in C++20.
  • 🛡️ 94% Adverse Selection Reduction: Proven in microsecond simulations to successfully dodge toxic sweeps, driving adverse selection losses down from $-\$0.52$ (naive symmetric) to $\$0.00$.
  • 🧠 Seamless Dual-Layer Integration: Bridged modern Deep Learning (PyTorch $\to$ ONNX) with closed-form Stochastic Calculus (Cartea-Jaimungal HJB PDE) without sacrificing microsecond execution constraints.
  • 📊 4-Way PnL Attribution: Built an institutional-grade decomposition engine isolating Spread Capture, Directional Alpha, Toxic Adverse Selection Drag, and Exchange Fees.
  • 🧪 100% Comprehensive Unit Test Coverage: Passed all GoogleTest C++ modules (OrderBook, OFI, QueueTracker, HJB solver, RiskManager) and PyTest Python suites (Time2Vec, CT-LiT, Dataset, Loss gradient backpropagation, ONNX parity).

What we learned

  • The Reality of Microstructure Latency: In high-frequency trading, a $25\,\mu\text{s}$ delay is an eternity. Having an alpha prediction is useless if your cancel/replace order sits in an in-flight queue while aggressive market sweeps execute.
  • The Interplay Between Alpha and Inventory Control: Alpha forecasting cannot operate in isolation. The optimal quote must balance inventory mean-reversion with directional anticipation—which the Cartea-Jaimungal HJB PDE unifies into a single closed-form solution.
  • Modern Low-Latency C++20 Architecture: Gained deep insights into CPU cache line alignment (alignas(64)), false sharing prevention, memory order semantics (std::memory_order_acquire/release), and fixed-point integer scaling.

What's next for Alpha-Skewed Optimal Market Making Engine

  • 🌐 Direct Exchange Connectivity: Implementing native binary feed handlers (NASDAQ ITCH/OUCH, CME MDP 3.0 SBE, Binance WebSocket) and kernel-bypass networking via Solarflare OpenOnload / DPDK.
  • ⚡ FPGA Hardware Acceleration: Porting the spatial patch projector and fixed-point HJB pricing kernels to Xilinx Vitis HLS / Verilog for sub-microsecond tick-to-trade execution.
  • 🔄 Multi-Asset Cross-Impact Modeling: Extending the CT-LiT Transformer to ingest multi-asset L2 books to capture lead-lag cross-asset alpha (e.g., BTC/USDT lead-lag on ETH/USDT).
  • 🤖 Reinforcement Learning Meta-Controller: Training an upper-level PPO/SAC reinforcement learning agent to dynamically calibrate risk aversion $\gamma$ and liquidity parameters $\kappa$ across changing market volatility regimes.
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