Proper Avellaneda-Stoikov: reservation price + optimal spread model

strategies/as_quoter.py

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+"""
+Proper Avellaneda-Stoikov market making for the live node.
+
+Key formulas (Avellaneda & Stoikov, 2008):
+  Reservation price:  r = s - q * gamma * sigma^2 * tau
+  Optimal spread:     spread = gamma * sigma^2 * tau + (2/gamma) * ln(1 + gamma/k)
+  Bid = r - spread/2    Ask = r + spread/2
+
+Where:
+  s = mid price, q = inventory, gamma = risk aversion
+  sigma = volatility, tau = remaining session time, k = order intensity
+
+Production adaptations:
+  - Rolling volatility estimation (5-min window)
+  - Circuit breaker: pause quoting when price jump exceeds 3σ
+  - Inventory bounds: stop quoting on over-exposed side
+  - Virtual session clock: 1-hour windows since crypto is 24/7
+"""
+
+import math
+from collections import deque
+
+
+class ASQuoter:
+    """Stateless per-tick quote generator using A-S optimal control."""
+
+    def __init__(
+        self,
+        gamma: float = 0.1,       # Risk aversion — higher = more aggressive inventory redux
+        k: float = 1.5,            # Order flow sensitivity — higher = tighter market
+        tau: float = 1.0,          # Virtual session length (hours, for 24/7 crypto)
+        min_spread: float = 0.0001, # 1 bp minimum spread
+        max_inventory: float = 0.001,  # Max position before stopping one side
+        vol_window: int = 300,     # Number of price ticks for rolling vol (5 min @ 1s)
+        cb_mult: float = 3.0,      # Circuit breaker multiplier (3σ jump threshold)
+    ):
+        self.gamma = gamma
+        self.k = k
+        self.tau = tau
+        self.min_spread = min_spread
+        self.max_inventory = max_inventory
+        self.vol_window = vol_window
+        self.cb_mult = cb_mult
+
+        self._mid_prices: deque[float] = deque(maxlen=vol_window)
+        self._current_sigma: float = 0.02  # fallback: ~32% annualized for crypto
+        self._session_start: float = 0.0
+
+    def observe(self, mid: float) -> None:
+        """Feed a new mid-price observation. Updates rolling volatility."""
+        self._mid_prices.append(mid)
+        if len(self._mid_prices) >= 2:
+            prices = list(self._mid_prices)
+            returns = [
+                (prices[i] - prices[i - 1]) / prices[i - 1]
+                for i in range(1, len(prices))
+            ]
+            mu = sum(returns) / len(returns)
+            var = sum((r - mu) ** 2 for r in returns) / len(returns)
+            sigma = math.sqrt(var) if var > 0 else 0.02
+            self._current_sigma = sigma
+
+    @property
+    def sigma(self) -> float:
+        return self._current_sigma
+
+    def circuit_breaker(self) -> bool:
+        """Check if recent price jump exceeds threshold. If true, pause quoting."""
+        if len(self._mid_prices) < 5:
+            return False
+        recent = list(self._mid_prices)[-5:]
+        move_pct = abs(recent[-1] - recent[0]) / recent[0]
+        threshold = self.cb_mult * self._current_sigma * math.sqrt(5)
+        return move_pct > threshold
+
+    def quotes(self, mid: float, inventory: float, t: float) -> dict | None:
+        """
+        Generate bid/ask quotes given current state.
+        
+        Args:
+            mid: current mid-price
+            inventory: current net position (positive = long)
+            t: elapsed session time in hours (0 to tau)
+        
+        Returns:
+            {"bid": ..., "ask": ..., "reservation": ..., "spread": ...} or None if paused
+        """
+        self.observe(mid)
+
+        if self.circuit_breaker():
+            return None  # Pause quoting — price jump in progress
+
+        # Reservation price: skew center by inventory risk
+        tau_remaining = max(self.tau - t, 0.01)
+        reservation = mid - inventory * self.gamma * (self._current_sigma ** 2) * tau_remaining
+
+        # Optimal spread: balance risk compensation vs flow capture
+        try:
+            log_term = math.log(1.0 + self.gamma / self.k)
+        except ValueError:
+            log_term = 0.0
+        spread = (
+            self.gamma * (self._current_sigma ** 2) * tau_remaining
+            + (2.0 / max(self.gamma, 0.001)) * log_term
+        )
+        spread = max(spread, self.min_spread)
+
+        half = spread / 2.0
+        bid = reservation - half
+        ask = reservation + half
+
+        return {
+            "bid": max(bid, 1.0),   # Never negative/zero
+            "ask": max(ask, 1.0),
+            "reservation": reservation,
+            "spread": spread,
+        }