{"slug":"the-heston-model-and-the-volatility-smile","qid":"cross_skew","label":"Put-side versus call-side implied volatility, 20 to 45 days (Jan to Jun 2026)","post_title":"Heston Model and the Volatility Smile","post_url":"/blog/the-heston-model-and-the-volatility-smile#q-cross_skew","columns":["symbol","otm_put_iv_pct","otm_call_iv_pct","put_minus_call_pts"],"rows":[{"symbol":"SPY","otm_put_iv_pct":27,"otm_call_iv_pct":14.76,"put_minus_call_pts":12.23},{"symbol":"AAPL","otm_put_iv_pct":34.86,"otm_call_iv_pct":26.25,"put_minus_call_pts":8.61},{"symbol":"NVDA","otm_put_iv_pct":47.89,"otm_call_iv_pct":40.13,"put_minus_call_pts":7.77},{"symbol":"AMZN","otm_put_iv_pct":41.96,"otm_call_iv_pct":35.49,"put_minus_call_pts":6.47},{"symbol":"KO","otm_put_iv_pct":27.38,"otm_call_iv_pct":21.29,"put_minus_call_pts":6.09},{"symbol":"MSFT","otm_put_iv_pct":36.82,"otm_call_iv_pct":32.92,"put_minus_call_pts":3.9}],"shape":"ranking","sql":"SELECT\n    underlying_symbol                                                    AS symbol,\n    round(avgIf(iv, ratio <= 0.95) * 100, 2)                             AS otm_put_iv_pct,\n    round(avgIf(iv, ratio >= 1.05) * 100, 2)                             AS otm_call_iv_pct,\n    round((avgIf(iv, ratio <= 0.95) - avgIf(iv, ratio >= 1.05)) * 100, 2) AS put_minus_call_pts\nFROM\n(\n    SELECT\n        underlying_symbol,\n        implied_volatility                                    AS iv,\n        toFloat64(strike_price) / toFloat64(underlying_close) AS ratio\n    FROM global_markets.options_greeks\n    WHERE underlying_symbol IN ('SPY', 'AAPL', 'MSFT', 'NVDA', 'AMZN', 'KO')\n      AND date BETWEEN '2026-01-02' AND '2026-06-30'\n      AND iv_converged = 1\n      AND volume > 0\n      AND days_to_expiry BETWEEN 20 AND 45\n      AND abs(toFloat64(strike_price) / toFloat64(underlying_close) - 1) <= 0.20\n)\nGROUP BY underlying_symbol\nHAVING countIf(ratio <= 0.95) > 0\n   AND countIf(ratio >= 1.05) > 0\nORDER BY put_minus_call_pts DESC","computed_at":"2026-08-12T15:51:34.569621+00:00","elapsed":0.003566132}