{
    "inputs": {
        "spot": 580,
        "strike": 580,
        "dte": 30,
        "sigma": 0.18,
        "premium": 12.69,
        "mu": 0.12,
        "type": "call",
        "risk_free_rate": 0.045,
        "dividend_yield": 0.013
    },
    "sizing": {
        "kelly_fraction": 0.076842,
        "half_kelly": 0.038421,
        "quarter_kelly": 0.01921,
        "kelly_pct": 7.68,
        "half_kelly_pct": 3.84
    },
    "analysis": {
        "expected_roi": 0.160546,
        "expected_roi_pct": 16.05,
        "expected_payoff": 14.7273,
        "probability_of_profit": 0.391739,
        "probability_of_profit_pct": 39.17,
        "probability_itm": 0.557494,
        "probability_itm_pct": 55.75,
        "max_loss": 12.69,
        "breakeven": 592.69,
        "expected_growth_rate": 0.00584368
    },
    "recommendation": "Risk 3.8% of bankroll (half-Kelly). Probability of profit: 39.2%. Expected ROI: 16.1%."
}