Proper A-S: side selection via reservation price (not spread formula)
The AS optimal spread formula gives absurd spreads at crypto scale. Real market makers quote at the MARKET spread (best bid/ask) and use AS to decide WHEN to quote based on inventory-adjusted fair value: r = s - q * gamma * sigma^2 * tau If r < best_bid (long-biased) → stop quoting bid If r > best_ask (short-biased) → stop quoting ask If circuit breaker active → pause both sides Decoupled: spread is market-driven, inventory skew is AS-driven.
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ramseshk
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"""
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Proper Avellaneda-Stoikov market making for the live node.
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Production Avellaneda-Stoikov market making for crypto.
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Key formulas (Avellaneda & Stoikov, 2008):
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Reservation price: r = s - q * gamma * sigma^2 * tau
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Optimal spread: spread = gamma * sigma^2 * tau + (2/gamma) * ln(1 + gamma/k)
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Bid = r - spread/2 Ask = r + spread/2
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Key insight (missed by most naive implementations):
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The AS formula does NOT tell you what price to quote.
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The market spread is determined by competition (best bid/ask).
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AS tells you WHEN to quote each side based on your inventory risk.
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Where:
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s = mid price, q = inventory, gamma = risk aversion
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sigma = volatility, tau = remaining session time, k = order intensity
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When you're long → reservation price drops below mid → stop quoting bid
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When you're short → reservation price rises above mid → stop quoting ask
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When flat → quote both sides symmetrically at market best bid/ask
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Production adaptations:
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- Rolling volatility estimation (5-min window)
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- Circuit breaker: pause quoting when price jump exceeds 3σ
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- Inventory bounds: stop quoting on over-exposed side
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- Virtual session clock: 1-hour windows since crypto is 24/7
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The AS math you paid attention to:
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r = s - q * gamma * sigma^2 * tau
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Your inventory-adjusted fair value. Compare to market prices.
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- If r < best_bid: you're overpriced on the buy side → don't bid
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- If r > best_ask: you're underpriced on the sell side → don't ask
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This is what Citadel, Jane Street, and every serious MM does.
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Quote at market, pick sides based on inventory.
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"""
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import math
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from collections import deque
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class ASQuoter:
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"""Stateless per-tick quote generator using A-S optimal control."""
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class ASMarketMaker:
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"""Avellaneda-Stoikov: pick quoting sides based on inventory-adjusted fair value."""
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def __init__(
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self,
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gamma: float = 0.1, # Risk aversion — higher = more aggressive inventory redux
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k: float = 1.5, # Order flow sensitivity — higher = tighter market
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tau: float = 1.0, # Virtual session length (hours, for 24/7 crypto)
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min_spread: float = 0.0001, # 1 bp minimum spread
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max_inventory: float = 0.001, # Max position before stopping one side
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vol_window: int = 300, # Number of price ticks for rolling vol (5 min @ 1s)
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cb_mult: float = 3.0, # Circuit breaker multiplier (3σ jump threshold)
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gamma: float = 0.1, # Risk aversion
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tau: float = 1.0, # Session length (hours)
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max_inventory: float = 0.003, # Max position (3x trade size for BTC)
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vol_window: int = 300,
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cb_mult: float = 3.0,
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):
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self.gamma = gamma
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self.k = k
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self.tau = tau
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self.min_spread = min_spread
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self.max_inventory = max_inventory
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self.vol_window = vol_window
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self.cb_mult = cb_mult
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self._mid_prices: deque[float] = deque(maxlen=vol_window)
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self._current_sigma: float = 0.02 # fallback: ~32% annualized for crypto
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self._session_start: float = 0.0
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self._prices: deque[float] = deque(maxlen=vol_window)
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self._sigma: float = 0.01 # fallback: 1% return vol
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# ── Vol estimation ──
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def observe(self, mid: float) -> None:
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"""Feed a new mid-price observation. Updates rolling volatility."""
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self._mid_prices.append(mid)
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if len(self._mid_prices) >= 2:
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prices = list(self._mid_prices)
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returns = [
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(prices[i] - prices[i - 1]) / prices[i - 1]
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for i in range(1, len(prices))
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]
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self._prices.append(mid)
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if len(self._prices) >= 10:
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prices = list(self._prices)
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returns = [(prices[i] - prices[i-1]) / prices[i-1] for i in range(1, len(prices))]
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mu = sum(returns) / len(returns)
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var = sum((r - mu) ** 2 for r in returns) / len(returns)
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sigma = math.sqrt(var) if var > 0 else 0.02
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self._current_sigma = sigma
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sigma = math.sqrt(var) if var > 0 else 0.01
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self._sigma = max(sigma, 0.001)
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@property
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def sigma(self) -> float:
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return self._current_sigma
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return self._sigma
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def circuit_breaker(self) -> bool:
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"""Check if recent price jump exceeds threshold. If true, pause quoting."""
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if len(self._mid_prices) < 5:
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if len(self._prices) < 5:
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return False
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recent = list(self._mid_prices)[-5:]
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recent = list(self._prices)[-5:]
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move_pct = abs(recent[-1] - recent[0]) / recent[0]
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threshold = self.cb_mult * self._current_sigma * math.sqrt(5)
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return move_pct > threshold
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return move_pct > self.cb_mult * self._sigma * math.sqrt(5)
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def quotes(self, mid: float, inventory: float, t: float) -> dict | None:
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# ── Side selection ──
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def should_quote(self, mid: float, best_bid: float, best_ask: float, inventory: float, t: float) -> dict:
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"""
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Generate bid/ask quotes given current state.
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Args:
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mid: current mid-price
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inventory: current net position (positive = long)
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t: elapsed session time in hours (0 to tau)
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Determine which sides to quote.
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Returns:
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{"bid": ..., "ask": ..., "reservation": ..., "spread": ...} or None if paused
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{"quote_bid": bool, "quote_ask": bool}
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Logic: compute reservation price. If it's below best_bid (you're long-biased),
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stop quoting bid. If it's above best_ask (you're short-biased), stop quoting ask.
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"""
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self.observe(mid)
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# Hard inventory bounds — never exceed max position
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if abs(inventory) >= self.max_inventory:
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if inventory > 0:
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return {"quote_bid": False, "quote_ask": True} # Only sell
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else:
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return {"quote_bid": True, "quote_ask": False} # Only buy
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# Circuit breaker — pause both sides
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if self.circuit_breaker():
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return None # Pause quoting — price jump in progress
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return {"quote_bid": False, "quote_ask": False}
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# Reservation price: skew center by inventory risk
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tau_remaining = max(self.tau - t, 0.01)
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reservation = mid - inventory * self.gamma * (self._current_sigma ** 2) * tau_remaining
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# Reservation price (return terms → convert to price)
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tau_rem = max(self.tau - t, 0.01)
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# Use notional inventory for meaningful skew
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q_notional = inventory * mid
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# Scale gamma for crypto: multiply by mid for effective skew
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gamma_eff = self.gamma * 500 # tuned for ~$100 allocation scale
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reservation = mid - q_notional * gamma_eff * (self._sigma ** 2) * tau_rem
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# Optimal spread: balance risk compensation vs flow capture
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try:
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log_term = math.log(1.0 + self.gamma / self.k)
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except ValueError:
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log_term = 0.0
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spread = (
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self.gamma * (self._current_sigma ** 2) * tau_remaining
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+ (2.0 / max(self.gamma, 0.001)) * log_term
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)
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spread = max(spread, self.min_spread)
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half = spread / 2.0
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bid = reservation - half
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ask = reservation + half
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# Side selection: only quote when reservation agrees
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quote_bid = reservation >= best_bid # We value the asset enough to buy
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quote_ask = reservation <= best_ask # We'd sell at or above our fair value
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return {
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"bid": max(bid, 1.0), # Never negative/zero
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"ask": max(ask, 1.0),
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"quote_bid": quote_bid,
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"quote_ask": quote_ask,
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"reservation": reservation,
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"spread": spread,
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"sigma": self._sigma,
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}
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