- average |inventory| vs. fixed spread, AAPL
- −82%
- average |inventory| vs. fixed spread, MSFT
- −88%
- average |inventory| vs. fixed spread, NVDA
- −50%
The question
The Avellaneda–Stoikov model shifts a market maker's reservation price against its inventory: long inventory pushes quotes down to encourage selling, short inventory pushes them up. The project starts from a pure Brownian simulation and replaces the simulated path with real one-minute bars, to see how the idea behaves on actual prices.
Approach
- Data. One-minute regular-session bars for AAPL, MSFT, and NVDA on 29 May 2026, with the bar close as a mid-price proxy.
- Calibration. Starting price, bar interval, and volatility come from each ticker's path; risk aversion, fill-intensity parameters, and the inventory limit are held as controlled assumptions, because bars cannot reveal true order arrival rates.
- Fills. Both strategies share the same fill model,
λ(δ) = A·e−kδ: quotes closer to mid fill more often. - Benchmark. A naive market maker with a fixed half-spread that never adjusts for inventory.
Results
| Ticker | Day return | Avg |inv| A–S | Avg |inv| naive | P&L A–S | P&L naive |
|---|---|---|---|---|---|
| AAPL | −0.56% | 1.78 | 9.85 | −5.17 | 51.32 |
| MSFT | +3.03% | 0.88 | 7.33 | −19.10 | 62.82 |
| NVDA | −0.71% | 1.24 | 2.49 | 27.14 | 39.09 |
The fixed-spread quoter earned more raw P&L on all three names, but it did so by carrying two to eight times as much inventory. On MSFT, which rose about 3% during the day, much of the naive strategy's profit was directional exposure it never meant to take. NVDA is the honest counterexample: there the inventory-aware strategy was profitable but had the larger drawdown, so the risk-control edge is not automatic.
What I learned
Market making should not be judged on final P&L alone. A strategy that earns more by holding a larger position is taking a different risk, not doing the same job better.
Next
More sessions and averaged results, parameter sweeps over risk aversion and fill intensity, fees and rebates, and real bid/ask or order-book data so fill rates can be estimated rather than assumed.