How a Brier bot quotes a market

Everything starts with one number: the price at which the bot is indifferentto trading. Not the market mid — the bot's own fair value, shifted by how much inventory it is already holding. Avellaneda & Stoikov (2008) gave the canonical form:

r = s − q · γ · σ² · (T − t)

If the bot is long, r drops below mid → it quotes to sell. If short, r rises above mid → it quotes to buy. The bot is always leaning back toward flat. That lean is the whole game.

The total distance between bid and ask comes from two terms:

δ = γ · σ² · (T − t)  +  (2/γ) · ln(1 + γ/κ)

The first term widens the spread when the world is volatile. The second is the structural profit of being the liquidity provider — it persists even if the bot is risk-neutral. κ measures how much traders chase price: low κ means they'll cross a wide spread, high κ means they won't.

Prediction markets settle at exactly $0 or $1. There is no hedge for "the probability Trump wins" — no underlying to short. So inventory risk is managed by hard limits. Guéant–Lehalle–Fernandez-Tapia (2013) bound it:

|q| ≤ Q

As the bot approaches Q, its spreads widen automatically; at Q, quotes disappear. Short 100k YES at $0.40 and the market resolves YES? You owe $100k, collected $40k → −$60k from one market. Q is what stops that.

Some of the people hitting your quote know more than you — campaign staff with private polls, an athlete who knows their own injury. The spread is the tax that lets you survive trading against them. Glosten–Milgrom (1985): at a coin-flip price, the minimum spread equals the fraction of informed flow.

spread(p = 0.5) ≈ μ

Brier watches VPIN (volume-synchronized probability of informed trading) as a real-time toxicity alarm. When buy/sell flow goes sharply imbalanced, informed money is arriving — the bot widens or pulls quotes before it gets cleaned out.

• › Bounded prices. Quote in log-odds space, not raw price — guarantees quotes stay inside (0, 1).
• › Terminal settlement. Price must converge to 0 or 1. Volatility undergoes a phase transition near resolution.
• › Event jumps. A goal, a ruling, a call — prices jump. Needs jump-diffusion, not smooth Brownian motion.
• › No delta-hedge. The "underlying" is an unobservable probability. Risk is managed by spread, limits, and cross-market hedges only.

The executor combines four layers on every quote:

The most important latency metric is not placing orders — it is cancellingthem before an informed trader fills a stale quote. Brier's safety stack:

• › Staged withdrawal — spreads widen as resolution nears; in the final minutes, quotes are fully pulled.
• › GTD orders — auto-expire before known high-impact events (Fed prints, election calls).
• › cancelAll() — halts every outstanding order on a position breach or toxicity spike.