added fair_prob.py

fair_prob.py

@@ -0,0 +1,38 @@
+from __future__ import annotations
+
+import math
+
+
+def _norm_cdf(z: float) -> float:
+    # Standard normal CDF via erf (no scipy dependency)
+    return 0.5 * (1.0 + math.erf(z / math.sqrt(2.0)))
+
+
+def fair_prob_threshold(
+    *,
+    spot: float,
+    strike: float,
+    sigma_per_second: float,
+    time_remaining_seconds: float,
+    resolves_yes_if_spot_ge_strike: bool,
+) -> float:
+    """
+    Conservative approximation:
+      spot(t) ~ Normal(spot, spot*sigma*sqrt(t))
+    and compute P(spot_T >= strike) or P(spot_T <= strike).
+    """
+    if spot <= 0 or strike <= 0:
+        return 0.5
+    t = max(1.0, float(time_remaining_seconds))
+    sigma = max(1e-9, float(sigma_per_second))
+    stdev = spot * sigma * math.sqrt(t)
+    if stdev <= 0:
+        return 0.5
+
+    z = (spot - strike) / stdev
+    p_ge = _norm_cdf(z)  # P(spot_T >= strike)
+
+    fair = p_ge if resolves_yes_if_spot_ge_strike else (1.0 - p_ge)
+
+    # clip away from certainty (tail risk)
+    return max(0.03, min(0.97, fair))