#Edge Math

#Definitions

• q — Market price (implied probability)
• p — Model probability
• σ — Model uncertainty (rolling std of p over last N updates, floor 2%)
• p_low — p − z×σ (z=1.28 for ~90% one-sided)
• edge_low — p_low − q
• time_mult — From distance_to_strike vs expected_move(time_left)
• exec_cost — Fees + slippage + spread penalty

#Robust Edge Formula

robust_edge = edge_low × time_mult − exec_cost
robust_roi  = robust_edge / q
kelly       = (p_low − q) / (1 − q)

#Time Feasibility

expected_move = price × realized_vol × sqrt(time_remaining / base_interval)
z_score       = distance_to_strike / expected_move

Multiplier by z-score:

| z < 0.5 | z < 1 | z < 2 | else | |---------|-------|-------|------| | 1.0 | 0.7 | 0.35 | 0.1 |

#Recommendation Criteria

Recommend only when:

• robust_edge > 0
• robust_roi ≥ 0.10 (config)
• time_mult ≥ 0.35 (config)
• capped_kelly ≥ 0.25% bankroll (config)

#Execution Cost

• Fee: 2%
• Slippage: 0.5%
• Spread penalty: spread × 0.5