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25DEC26."],"history":[{"date":"2026-09-21","asOf":1790003914955,"spot":2742.38,"atm30":0.508705,"mf30":0.554363,"rv30":0.405382,"vrp30":14.8981,"vrpT30":2.8467,"rr30":2.11613,"bf30":1.67133,"dvol":0.5296,"headline":{"label":"25DEC26","level":3500,"p":0.146466},"medRmse":0.391059,"bfFails":0,"calFails":0},{"date":"2026-09-22","asOf":1790084325874,"spot":2749.87,"atm30":0.501241,"mf30":0.545334,"rv30":0.390019,"vrp30":15.5315,"vrpT30":3.08463,"rr30":1.75913,"bf30":1.39306,"dvol":0.5201,"headline":{"label":"25DEC26","level":3500,"p":0.145487},"medRmse":0.390538,"bfFails":0,"calFails":0},{"date":"2026-09-23","asOf":1790171396478,"spot":2714.52,"atm30":0.50245,"mf30":0.546646,"rv30":0.389638,"vrp30":15.7007,"vrpT30":3.12129,"rr30":0.343943,"bf30":1.47989,"dvol":0.5198,"headline":{"label":"25DEC26","level":3500,"p":0.134574},"medRmse":0.34467,"bfFails":0,"calFails":1},{"date":"2026-09-24","asOf":1790257525440,"spot":2665.03,"atm30":0.492787,"mf30":0.542726,"rv30":0.394366,"vrp30":14.836,"vrpT30":2.91402,"rr30":0.416904,"bf30":1.52355,"dvol":0.515,"headline":{"label":"25DEC26","level":3250,"p":0.181415},"medRmse":0.417939,"bfFails":0,"calFails":0},{"date":"2026-09-25","asOf":1790345312883,"spot":2681.82,"atm30":0.480876,"mf30":0.526621,"rv30":0.390605,"vrp30":13.6015,"vrpT30":2.69727,"rr30":0.530316,"bf30":1.42331,"dvol":0.5019,"headline":{"label":"25DEC26","level":3500,"p":0.119034},"medRmse":0.245615,"bfFails":0,"calFails":0},{"date":"2026-09-26","asOf":1790428908040,"spot":2686.86,"atm30":0.466473,"mf30":0.511476,"rv30":0.391086,"vrp30":12.039,"vrpT30":2.38448,"rr30":0.60143,"bf30":1.41736,"dvol":0.486,"headline":{"label":"25DEC26","level":3500,"p":0.118416},"medRmse":0.361597,"bfFails":0,"calFails":0},{"date":"2026-09-27","asOf":1790518569979,"spot":2707.09,"atm30":0.471923,"mf30":0.517494,"rv30":0.382939,"vrp30":13.4555,"vrpT30":2.72173,"rr30":0.81864,"bf30":1.41255,"dvol":0.4926,"headline":{"label":"25DEC26","level":3500,"p":0.122086},"medRmse":0.437815,"bfFails":0,"calFails":0},{"date":"2026-09-28","asOf":1790614749021,"spot":2685.86,"atm30":0.471857,"mf30":0.516306,"rv30":0.398313,"vrp30":11.7993,"vrpT30":2.29459,"rr30":0.332828,"bf30":1.41873,"dvol":0.4892,"headline":{"label":"25DEC26","level":3500,"p":0.116726},"medRmse":0.384907,"bfFails":0,"calFails":0},{"date":"2026-09-29","asOf":1790694200093,"spot":2706.52,"atm30":0.482421,"mf30":0.527296,"rv30":0.403627,"vrp30":12.367,"vrpT30":2.37334,"rr30":0.993201,"bf30":1.56177,"dvol":0.5048,"headline":{"label":"25DEC26","level":3500,"p":0.122047},"medRmse":0.451944,"bfFails":0,"calFails":0},{"date":"2026-09-30","asOf":1790781270390,"spot":2680.13,"atm30":0.479464,"mf30":0.528196,"rv30":0.404205,"vrp30":12.3991,"vrpT30":2.37609,"rr30":-0.482296,"bf30":1.57599,"dvol":0.5019,"headline":{"label":"25DEC26","level":3250,"p":0.179634},"medRmse":0.412394,"bfFails":0,"calFails":0},{"date":"2026-10-01","asOf":1790869112281,"spot":2678.28,"atm30":0.478101,"mf30":0.534425,"rv30":0.396193,"vrp30":13.8232,"vrpT30":2.70257,"rr30":0.203104,"bf30":1.80852,"dvol":0.5047,"headline":{"label":"25DEC26","level":3250,"p":0.175598},"medRmse":0.557487,"bfFails":0,"calFails":0},{"date":"2026-10-02","asOf":1790953046668,"spot":2708.03,"atm30":0.467206,"mf30":0.521011,"rv30":0.404672,"vrp30":11.6339,"vrpT30":2.22688,"rr30":0.689264,"bf30":1.77716,"dvol":0.4912,"headline":{"label":"25DEC26","level":3500,"p":0.115515},"medRmse":0.543327,"bfFails":0,"calFails":0},{"date":"2026-10-03","asOf":1791034838000,"spot":2681.01,"atm30":0.455294,"mf30":0.507238,"rv30":0.380587,"vrp30":12.6651,"vrpT30":2.57768,"rr30":-0.234686,"bf30":1.82604,"dvol":0.4796,"headline":{"label":"25DEC26","level":3250,"p":0.169814},"medRmse":0.689233,"bfFails":0,"calFails":0},{"date":"2026-10-04","asOf":1791123666023,"spot":2692.83,"atm30":0.469911,"mf30":0.524601,"rv30":0.376522,"vrp30":14.808,"vrpT30":3.04637,"rr30":0.320762,"bf30":1.90684,"dvol":0.4951,"headline":{"label":"25DEC26","level":3500,"p":0.107738},"medRmse":0.562713,"bfFails":0,"calFails":0},{"date":"2026-10-05","asOf":1791220948984,"spot":2699.48,"atm30":0.464014,"mf30":0.513795,"rv30":0.374717,"vrp30":13.9079,"vrpT30":2.87497,"rr30":0.368794,"bf30":1.64302,"dvol":0.487,"headline":{"label":"25DEC26","level":3500,"p":0.106286},"medRmse":0.380608,"bfFails":0,"calFails":0},{"date":"2026-10-06","asOf":1791300333018,"spot":2716.21,"atm30":0.453354,"mf30":0.502666,"rv30":0.373897,"vrp30":12.877,"vrpT30":2.66771,"rr30":-0.113216,"bf30":1.61045,"dvol":0.477,"headline":{"label":"25DEC26","level":3500,"p":0.108717},"medRmse":0.524958,"bfFails":0,"calFails":0},{"date":"2026-10-07","asOf":1791387903757,"spot":2563.82,"atm30":0.453462,"mf30":0.505013,"rv30":0.398466,"vrp30":10.6547,"vrpT30":2.07122,"rr30":-1.66382,"bf30":1.77697,"dvol":0.4751,"headline":{"label":"25DEC26","level":3250,"p":0.119219},"medRmse":0.372653,"bfFails":0,"calFails":0},{"date":"2026-10-08","asOf":1791474614779,"spot":2454.11,"atm30":0.48231,"mf30":0.541944,"rv30":0.425061,"vrp30":11.6883,"vrpT30"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term structure runs 47.9% at 11.8d to 53.2% at 341d, a +5.34 vol pts spread. Upward sloping: the market prices near-term calm against longer-dated uncertainty. Forward variance is being sold cheaply at the front and bid further out, which is the normal shape outside a stress episode.","Forward ATM variance is richest over 26MAR27–25JUN27 at 55.0% and cheapest over 22OCT26–23OCT26 at 46.5%. 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 -3.28 vol pts: the 25-delta put trades at 53.0% against 49.8% for the 25-delta call, on strikes $2,187 and $2,745 around a $2,424 forward. Negative: downside strikes are bid over equidistant upside. The market is paying a premium for protection, not for participation.","Across tenors RR25 moves from -10.52 vol pts at 0.8d to +0.40 vol pts at 341d. 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 +1.64 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. That is a moderate convexity charge.","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 -3.15 vol pts, the 7th 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 55.2% against 41.0% realized over the trailing 40 days: +14.15 vol pts of premium. In variance terms that is 0.1360, 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 17.16 vol pts — for iid returns SE(sigma) = sigma/sqrt(2n) — so 19OCT26's -3.38 vol pts is -0.2 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, +5.41 vol pts above ATM implied of 49.7%. 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.","Measured ex post over 377 overlapping 30-day windows, selling variance earned a mean +3.78 vol pts with a median of +8.78 vol pts, positive on 59.2% of days, dispersion 17.22 vol pts, 5th percentile -28.24 vol pts and worst case -43.37 vol pts. This is the premium the seller was PAID, comparing DVOL on each date with variance realized over the following 30 days.","Note the shape of that distribution rather than its mean. A 59.2% hit rate with a -43.37 vol pts worst case is the signature of a short-volatility payoff: it collects steadily and loses violently. The mean is a poor summary of a return series whose left tail is 11x its average gain.","Those 377 windows overlap: consecutive observations share 29 of their 30 days, so the series is close to a random walk in its own right and the nominal count is not the evidence. Dividing by the horizon leaves 12.6 independent windows, against which the mean carries a standard error of 4.86 vol pts and a t-statistic of 0.78. That does not clear conventional significance. Roughly a year of history is simply too short to establish a variance premium; the literature that does so uses decades.","The ex-ante series — implied against TRAILING realized, the only version observable in real time — averages +3.50 vol pts. The gap against the ex-post mean of +3.78 vol pts is the error from using past variance as a forecast of future variance, and it is the reason the live signal is weaker than the backtest.","Realized vol over the same trailing window by estimator: close-to-close 39.1%, Parkinson 47.1%, Garman-Klass 48.7%, Yang-Zhang 50.0%. 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 $2,405 against a forward of $2,433, with a 90% interval of $1,574 to $3,365 and an interquartile range of $2,105 to $2,723.","Level probabilities read directly off the digital, Q(S_T > X) = -e^{rT} dC/dK: $1,500 96.0%, $1,750 91.3%, $2,250 63.7%, $2,500 41.6%, $3,000 12.3%, $3,750 2.1%, $4,750 0.4%.","The distribution carries skewness 1.020 and excess kurtosis 7.041. 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 7.04 against 0 for a Gaussian is the market pricing fat tails on both sides.","Integrity of the density: total mass 0.999363 (target 1, error -6.4e-4) and mean $2,432 against a forward of $2,433, off by -1.19 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."],"diagnostics":["Calibration residuals: median slice RMSE 0.83 vol pts, worst 20OCT26 at 1.19 (core |k| <= 0.5: 1.19). 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 0.507 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."]}}