MicroExchange

Exchange-grade CLOB matching engine + ITCH-style market data replay + microstructure analytics in modern C++20.

📊 Live Interactive Dashboard — 3D order book surface, Kyle's lambda landscape, spread decomposition, stylized facts.

A complete market microstructure laboratory: from order entry to trade print, from raw event feeds to empirical spread decomposition, built with the rigor of production exchange systems and the analytical depth of graduate-level financial economics.

Visualizations

3D Limit Order Book Surface - Bid (blue) and ask (red) depth across price levels over time:

3D Price Impact Surface - Kyle's lambda: impact increases with volume (concave, square-root law) and amplifies with directional imbalance:

Spread Decomposition - Effective spread split into realized spread (MM revenue) and price impact. Real large-caps run ~50–70% adverse selection; this zero-intelligence sim produces ≈0 (uninformed flow → no permanent impact) - see reproducible results.

Stylized Facts - Return distribution vs Gaussian and the autocorrelation of |returns|. Reproduced on 1s bars: volatility clustering AC(|r|,1) ≈ 0.24; fat tails are mild (excess kurtosis ≈ 1.2) under zero-intelligence flow - see reproducible results.

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Architecture

  order sources                  matching core                      outputs
  ─────────────                  ─────────────                      ───────

  ┌──────────────┐
  │ TCP Gateway  │─┐   binary order-entry protocol over a socket (net/)
  └──────────────┘ │
  ┌──────────────┐ │   ┌─────────────────────────────┐    ┌──────────────────┐
  │ Simulation   │ ├──▶│      Matching Engine        │──▶ │ Market Data Feed │
  │ (Hawkes/ZI)  │ │   │ price-time priority (FIFO)  │    │ (ITCH-style:     │
  └──────────────┘ │   │ Limit/Market/IOC/FOK/Stop   │    │ incremental +    │
  ┌──────────────┐ │   │                             │    │ snapshots)       │
  │ ITCH Replay  │─┘   │ book backends (same API):   │    └──────────────────┘
  │ (historical) │     │  • OrderBook     (std::map) │    ┌──────────────────┐
  └──────────────┘     │  • ArrayOrderBook (array +  │──▶ │ Analytics        │
                       │     bitmap BBO index)       │    │ spread decomp,   │
                       └──────────────────────-──────┘    │ Kyle's λ, OFI,   │
                                                          │ stylized facts   │
                                                          └──────────────────┘

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Visualizations

→ Interactive 3D charts (GitHub Pages)

3D Order Book Surface — Depth × Price × Time

Bid side (blue) and ask side (red) form the characteristic valley around the midpoint. Depth clusters at key levels and shifts with the price drift.

3D Price Impact Surface — Kyle's λ Landscape

Price impact as a function of trade volume and order flow imbalance. The concave shape demonstrates the square-root law of impact (Bouchaud et al., 2018) - larger trades have diminishing marginal impact, amplified by directional imbalance.

Spread Decomposition — Huang-Stoll (1997)

Effective spread decomposed into realized spread (market maker revenue) and price impact. In liquid equities adverse selection is ~50-70%; under zero-intelligence flow it collapses to ≈0 (no informed trading), consistent with Kyle's λ ≈ 0. Reproducing realistic adverse selection requires informed agents (see Known Issues / future work).

Stylized Facts: Fat Tails & Volatility Clustering

Left: return distribution vs Gaussian - heavy tails from Hawkes-driven clustering. Right: autocorrelation of |returns| showing slow decay characteristic of ARCH effects.

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Order Types

| Type | TIF | Behaviour | |---|---|---| | Limit | GTC / DAY | Rests on the book at price. | | Market | IOC | Crosses the book at any price; unfilled remainder cancelled. | | IOC | IOC | Limit semantics; remainder after the first match is cancelled. | | FOK | FOK | Pre-checked for full fill; if not, never enters the book. | | Stop | - | Parked until last_trade_price crosses stop_price, then released as Market. | | StopLimit | - | Parked until trigger; released as Limit at price. |

Stops are stored in dedicated per-side multimaps keyed by trigger price. Every aggressive cycle that updates the last print runs a guarded check_stop_triggers() pass — releases are themselves matched immediately, which can cascade into more triggers without recursing on the call stack.

Microstructure Concepts Implemented

| Domain | Concept | Implementation | |--------|---------|---------------| | Market Structure | Price-time priority (FIFO) | core/OrderBook with deterministic sequencing | | Market Structure | Queue position tracking | Per-level FIFO queues with sequence numbers | | Liquidity | Quoted spread | Real-time BBO tracking in analytics/SpreadAnalyzer | | Liquidity | Effective spread | Trade-midpoint deviation analysis | | Liquidity | Depth & resilience | Post-trade book recovery metrics | | Price Formation | Realized spread | 5-second post-trade midpoint reversion | | Price Formation | Price impact (permanent) | Effective − Realized spread decomposition | | Information | Order flow imbalance (OFI) | Signed volume aggregation → return prediction | | Information | Kyle's λ | Regression: ΔP = λ · signed_volume + ε | | Adverse Selection | Glosten-Milgrom intuition | Spread widens with information asymmetry in simulation | | Inventory | Ho-Stoll / Avellaneda-Stoikov | Quote skewing under inventory risk in MM agent | | Stylized Facts | Fat tails, vol clustering | Hawkes arrival process + empirical verification | | Stylized Facts | Spread under stress | Endogenous widening with order imbalance |

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What Makes This Different

Most GitHub "matching engines" are toy implementations — a sorted map, a match loop, and a README. This project bridges three disciplines:

1. Systems engineering - Lock-free queues, arena allocation, cache-aligned structures, deterministic replay, property-based invariant testing
2. Financial economics - Spread decomposition, adverse selection models, information-based trading theory (Glosten-Milgrom, Kyle, Ho-Stoll)
3. Quantitative research - Reproducible empirical analysis, stylized fact generation, microstructure model calibration

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Known Issues & Limitations

• No informed traders → adverse selection ≈ 0: Agents are zero-intelligence, so order flow carries no private information. Both the Huang-Stoll decomposition (price impact ≈ 0) and Kyle's λ (R² ≈ 0.01) correctly report this. It is a modeling limitation, not a bug - reproducing realistic adverse selection (~50–70% of the spread) requires a Glosten-Milgrom-style informed-trader population. Tracked as future work.

• Fat tails are mild: on 1s bars the ZI midprice is contained (a ~15-tick range over the hour), so excess kurtosis is ~1.2 — present but below intraday equities. Deep tails need informed/trending flow or a fundamental-value process.

• Arena allocator never frees: Orders accumulate in the arena for the lifetime of the process. Fine for simulation (it exits) but would need periodic cleanup or epoch-based reclamation for production.

• No proper order tracking per agent: The cancellation logic in the simulator is approximate — agents don't track their own outstanding orders, so cancel rates are estimates.

• No iceberg / hidden-quantity orders yet. Refilling visible slices interacts with FIFO priority in a non-obvious way; tracked in CHANGELOG.md as future work.

• Visualization PNGs predate v1.2.0: the 3D surface images above are illustrative and were rendered before the analytics fixes below; the authoritative, reproducible numbers live in output/report.txt. Regenerating the figures from current output is tracked as future work.

Resolved in v1.2.0

• ~~Volatility clustering is weak (AC|r| ≈ 0.02)~~ — was a sampling artifact. Returns are now computed on fixed 1-second bars as log returns instead of per-event on the integer-tick mid; AC(|r|, lag 1) = 0.24, inside the empirical 0.15–0.40 range.
• ~~Excess kurtosis is a spurious 78~~ — same root cause (a return series that was ≈99% exact zeros). Time-bar log returns give a realistic 1.16.
• ~~Spread decomposition doesn't satisfy effective = realized + impact~~ — the price-impact term was averaged in absolute value while realized was signed. Now consistently signed, so the identity holds and the adverse-selection % is meaningful.

Resolved in v1.1.0

• ~~FeedPublisher overwrites OrderBook callbacks~~ — fixed by a multi-subscriber listener fan-out on OrderBook. The publisher is now re-enabled in main.cpp and reports message counts in the per-run report.
• ~~Kyle's lambda R² is near zero because of event-index bucketing~~ — the regression now uses Hawkes wall-clock timestamps for both trades and midprices. (R² is still low because ZI flow is uninformed — see above — but the bucketing is no longer the bottlene