AI Market-Maker: Optimal Quoting Simulator

Market-Maker Controls

Risk aversion γ 0.10

Order-flow decay κ 1.5

Volatility σ 0.30

Live State

Mid price S

100.00

Inventory q

Mark-to-market P&L

0.00

Quoted spread δ

0.00

Bid

99.90

Ask

100.10

How it works

This models a single dealer quoting both sides of the market for one asset, using the Avellaneda–Stoikov (2008) optimal market-making framework. The mid price S follows a random walk (volatility σ). Instead of quoting symmetrically around S, the agent quotes around a reservation price that skews away from its current inventory q, so it becomes eager to unload a long position and reluctant to buy more:

r(s,q,t) = s − q·γ·σ²·(T−t)
δ(t)     = γ·σ²·(T−t) + (2/γ)·ln(1 + γ/κ)
bid = r − δ/2,   ask = r + δ/2

γ is the dealer's risk aversion, (T−t) the time left in the trading session (the yellow bar), and κ controls how fast counterparty order flow decays with distance from the mid — a proxy for book liquidity, visualised as the fading depth ladder ahead of the price ribbon. Each tick, a fill at the bid or ask occurs with probability 1 − e^−λδt, where λ = A·e^{−κ·|quote − mid|}: quotes closer to the touch fill more often, wider ones rarely fill but bank more spread when they do.

γ ↑ — quotes skew harder away from inventory and widen, so risk is shed faster at the cost of P&L.
κ ↑ — counterparties are more price-sensitive, so the optimal spread narrows to compete for flow.
σ ↑ — holding inventory is riskier, so both the skew and the spread widen.
At the end of each session the agent's remaining inventory is closed at the mid price, realising any residual risk it was carrying — watch the P&L jump at each yellow-bar reset.

This is the same mechanism behind AI-driven market-making desks and automated liquidity provision in modern electronic and crypto exchanges.

Mid price S Reservation price r Bid quote Ask quote

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