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25DEC26."],"history":[{"date":"2026-09-21","asOf":1790003928179,"spot":118.176,"atm30":0.572999,"mf30":0.631251,"rv30":0.597654,"vrp30":3.35971,"vrpT30":0.435439,"rr30":4.24325,"bf30":2.7275,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.141682},"medRmse":0.641881,"bfFails":0,"calFails":0},{"date":"2026-09-22","asOf":1790084337449,"spot":117.356,"atm30":0.584139,"mf30":0.645521,"rv30":0.581143,"vrp30":6.43777,"vrpT30":0.858081,"rr30":4.39924,"bf30":2.6905,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.137279},"medRmse":0.508057,"bfFails":0,"calFails":0},{"date":"2026-09-23","asOf":1790171409970,"spot":116.746,"atm30":0.56259,"mf30":0.622318,"rv30":0.539603,"vrp30":8.27154,"vrpT30":1.18737,"rr30":3.57804,"bf30":2.5573,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.126229},"medRmse":0.513203,"bfFails":0,"calFails":0},{"date":"2026-09-24","asOf":1790257553223,"spot":114.714,"atm30":0.561444,"mf30":0.622105,"rv30":0.530762,"vrp30":9.1343,"vrpT30":1.33306,"rr30":4.14338,"bf30":2.80088,"dvol":null,"headline":{"label":"25DEC26","level":140,"p":0.167778},"medRmse":0.427081,"bfFails":0,"calFails":0},{"date":"2026-09-25","asOf":1790345327856,"spot":119.337,"atm30":0.541785,"mf30":0.609172,"rv30":0.510301,"vrp30":9.88714,"vrpT30":1.50079,"rr30":4.60988,"bf30":2.66165,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.140022},"medRmse":0.642195,"bfFails":0,"calFails":0},{"date":"2026-09-26","asOf":1790428918138,"spot":120.847,"atm30":0.536489,"mf30":0.587949,"rv30":0.495067,"vrp30":9.28822,"vrpT30":1.45326,"rr30":2.22822,"bf30":1.96892,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.150625},"medRmse":0.635445,"bfFails":0,"calFails":0},{"date":"2026-09-27","asOf":1790518585070,"spot":123.083,"atm30":0.548462,"mf30":0.597289,"rv30":0.497622,"vrp30":9.96669,"vrpT30":1.55141,"rr30":1.96161,"bf30":1.93933,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.171034},"medRmse":0.565957,"bfFails":0,"calFails":0},{"date":"2026-09-28","asOf":1790614758111,"spot":119.294,"atm30":0.539288,"mf30":0.595959,"rv30":0.52685,"vrp30":6.91092,"vrpT30":1.01607,"rr30":2.10201,"bf30":2.33002,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.141199},"medRmse":0.700966,"bfFails":0,"calFails":0},{"date":"2026-09-29","asOf":1790694209109,"spot":120.026,"atm30":0.565334,"mf30":0.616611,"rv30":0.523817,"vrp30":9.27935,"vrpT30":1.37219,"rr30":3.23576,"bf30":2.26927,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.149985},"medRmse":0.541632,"bfFails":0,"calFails":0},{"date":"2026-09-30","asOf":1790781285076,"spot":118.857,"atm30":0.554346,"mf30":0.614568,"rv30":0.524667,"vrp30":8.99008,"vrpT30":1.32726,"rr30":3.08975,"bf30":2.37171,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.137386},"medRmse":0.672702,"bfFails":0,"calFails":0},{"date":"2026-10-01","asOf":1790869130235,"spot":117.268,"atm30":0.536211,"mf30":0.601306,"rv30":0.51256,"vrp30":8.87453,"vrpT30":1.34115,"rr30":2.69742,"bf30":2.4316,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.127281},"medRmse":0.615731,"bfFails":0,"calFails":0},{"date":"2026-10-02","asOf":1790953064437,"spot":120.643,"atm30":0.532108,"mf30":0.578274,"rv30":0.528055,"vrp30":5.02197,"vrpT30":0.736666,"rr30":4.06864,"bf30":1.5047,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.144098},"medRmse":0.360021,"bfFails":0,"calFails":0},{"date":"2026-10-03","asOf":1791034851120,"spot":119.604,"atm30":0.528418,"mf30":0.586838,"rv30":0.51991,"vrp30":6.6928,"vrpT30":0.997138,"rr30":3.26271,"bf30":2.18802,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.138023},"medRmse":0.46876,"bfFails":0,"calFails":0},{"date":"2026-10-04","asOf":1791123678923,"spot":121.331,"atm30":0.534603,"mf30":0.585673,"rv30":0.520518,"vrp30":6.51553,"vrpT30":0.969594,"rr30":3.25756,"bf30":2.04375,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.148851},"medRmse":0.427033,"bfFails":0,"calFails":0},{"date":"2026-10-05","asOf":1791220970118,"spot":119.711,"atm30":0.517048,"mf30":0.567348,"rv30":0.513505,"vrp30":5.38424,"vrpT30":0.812185,"rr30":2.31048,"bf30":2.13362,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.135976},"medRmse":0.441453,"bfFails":0,"calFails":0},{"date":"2026-10-06","asOf":1791300350193,"spot":121.459,"atm30":0.520454,"mf30":0.563099,"rv30":0.51273,"vrp30":5.03697,"vrpT30":0.760951,"rr30":2.4611,"bf30":1.80924,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.146477},"medRmse":0.364236,"bfFails":0,"calFails":0},{"date":"2026-10-07","asOf":1791387915138,"spot":116.552,"atm30":0.503327,"mf30":0.558455,"rv30":0.514509,"vrp30":4.3946,"vrpT30":0.661609,"rr30":2.67068,"bf30":2.37388,"dvol":null,"headline":{"label":"25DEC26","level":150,"p":0.104012},"medRmse":0.710942,"bfFails":0,"calFails":0},{"date":"2026-10-08","asOf":1791474626226,"spot":109.475,"atm30":0.501613,"mf30":0.554734,"rv30":0.546378,"vrp30":0.835641,"vrpT30":0.118468,"rr30":0.0245222,"bf30":2.00666,"dvol":null,"headl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term structure runs 55.4% at 11.8d to 53.7% at 68d, a -1.79 vol pts spread. Inverted: near-dated variance is bid above longer-dated. Term-structure inversion is a stress signature — an identified near-term event, or spot already moving — and it typically mean-reverts faster than the level of vol does.","Forward ATM variance is richest over 20OCT26–23OCT26 at 58.6% and cheapest over 27NOV26–25DEC26 at 52.9%. Forward vol strips out the variance already priced into the nearer expiry, so it isolates what the market charges for that interval alone — the calendar-spread signal that the raw term structure hides."],"skew":["RR25 at the 40-day tenor is +0.70 vol pts: the 25-delta put trades at 57.0% against 57.7% for the 25-delta call, on strikes $94 and $121 around a $104 forward. Near zero: the market is charging symmetrically for both tails.","Across tenors RR25 moves from -2.32 vol pts at 1.8d to +2.10 vol pts at 68d. Skew is steepest at the front: the market is pricing a near-term downside event and expects the asymmetry to decay.","BF25 at the same tenor is +3.22 vol pts, the average 25-delta wing over the ATM. Butterfly prices convexity — the cost of a large move in either direction — and is the part of the smile that RR25, being a difference, cannot see. At this level the market is paying materially for tails on both sides.","Read RR25 as a difference, not a level: it is nearly immune to the overall vol level, so it moves when the market re-prices ASYMMETRY rather than when it re-prices risk. A doubling of ATM vol in a rally can leave RR25 untouched; a funding scare shows up in it immediately.","At 30-day constant maturity RR25 reads -0.02 vol pts, the 15th percentile of the last 27 daily readings. That percentile, not the level, is the fear gauge: it says whether today's asymmetry is unusual for this market."],"vrp":["At the 40-day tenor the fair variance-swap strike is 63.0% against 51.4% realized over the trailing 40 days: +11.62 vol pts of premium. In variance terms that is 0.1330, which is the quantity a variance swap actually settles on.","The short-tenor premiums are not measurements. Realized vol over a 5-day window carries a standard error of 14.75 vol pts — for iid returns SE(sigma) = sigma/sqrt(2n) — so 20OCT26's +9.83 vol pts is 0.7 standard errors of the realized leg alone. Anything under roughly 2 there is a quiet sample, not an edge, and the front of this curve should be read as an implied level rather than as a premium.","The implied leg is the model-free strike, +8.87 vol pts above ATM implied of 54.2%. That gap is the convexity of the smile, and it is why using ATM vol for the implied leg understates the premium systematically rather than randomly.","Realized vol over the same trailing window by estimator: close-to-close 47.9%, Parkinson 58.8%, Garman-Klass 61.7%, Yang-Zhang 61.8%. Close-to-close is the reference here because it is what a variance swap settles on; the range-based estimators are more efficient but measure a different functional, and the spread between them is itself a read on whether the move is trending or choppy."],"density":["Over 68 days to 25DEC26, the option-implied distribution puts its median at $102 against a forward of $105, with a 90% interval of $66 to $149 and an interquartile range of $90 to $117.","Level probabilities read directly off the digital, Q(S_T > X) = -e^{rT} dC/dK: $60 96.5%, $80 87.0%, $90 74.5%, $100 55.2%, $130 12.2%, $160 3.3%, $210 0.7%.","The distribution carries skewness 2.219 and excess kurtosis 19.200. Positive skew in the RND is the arithmetic consequence of lognormality — price cannot go below zero but has no ceiling — and does NOT mean the market expects a rally. The market's directional fear lives in RR25, not in the sign of this moment. Excess kurtosis of 19.20 against 0 for a Gaussian is the market pricing fat tails on both sides.","Integrity of the density: total mass 0.998992 (target 1, error -1.0e-3) and mean $105 against a forward of $105, off by -4.47 bp. The second is the sharper test: under Q the forward is a martingale, so the density's mean MUST be the forward, and any drift there would mean the calibration is not arbitrage-consistent.","2.19% of the probability mass falls outside the quoted strike range $50–$240. Inside that range the density reads market prices; outside it reads SVI's linear-in-variance wing extrapolation. Tail probabilities beyond the listed strikes are a model output, not a market observation."],"diagnostics":["Calibration residuals: median slice RMSE 0.59 vol pts, worst 30OCT26 at 0.71 (core |k| <= 0.5: 0.71). Residuals are quoted in vol points so they can be compared against the bid-ask width, which is the only benchmark that decides whether a fit is good enough to trade on.","Butterfly: Durrleman's g(k) >= 0 on every slice, so the implied density is non-negative everywhere and the Breeden-Litzenberger output is well defined.","Calendar: total variance is non-decreasing in maturity across every adjacent pair, so the surface admits no calendar-spread arbitrage and interpolation in T is monotone.","Wing slopes peak at 0.184 against Roger Lee's bound of 2. Total variance growing faster than 2|k| in the wings would imply a distribution with no finite moment of the corresponding order, so this bound is a hard consistency requirement, not a preference."]}}