BTC: Options-Implied Price Percentiles (90 Days)
Shown as its 2–31 Oct 2026 sample; the latest readings and full history are included with Plus.
The BTC prices options put at the 10th, 25th, 50th, 75th and 90th percentiles 90 days ahead, at each snapshot: the price distribution the options market is pricing.
Why use it. Turns the whole volatility smile, skew included, into price levels: where options put the middle half and the middle 80% of outcomes 90 days out, and whether the downside or the upside is priced wider. How to read it. Half of the priced outcomes lie between the 25th and 75th percentile lines and 80% between the 10th and 90th. A lower band further below the median than the upper band is above it shows the market paying more for downside. Compare later prices with the lines drawn 90 days earlier. These are probabilities priced into options (risk-neutral), not a forecast: they include what traders pay for protection.
Calculation. For each expiry's fitted smile, the chance of ending above a price K is minus the slope of the call price in K (the price of a digital call): N(d2) - n(d2) w'(k) / (2 sqrt(w)), with w(k) the fitted total variance at k = ln(K / forward) and d2 = -k / sqrt(w) - sqrt(w) / 2 (Black-76, rates zero). N(d2) alone would ignore the smile's slope. A percentile is the price where that chance equals one minus the percentile, found by bisection, and only inside the strikes the fit covers. Only fits that pass the butterfly and variance checks are used, and each is checked again: the chance must fall as the price rises. 90 days: total variance interpolated linearly in time at each k, and the forward in log terms, between the nearest expiries around 90 days whose quoted strikes reach the 10th and 90th percentiles; when none do (a newly listed expiry or the weeklies can quote a narrow run of strikes), the 10th and 90th are left out of that reading and the others come from the nearest pair that reaches the 25th and 75th. Fit: for each expiry more than a day away, a raw SVI smile, total implied variance w(k) = a + b (rho (k - m) + sqrt((k - m)^2 + sigma^2)) with w = IV^2 x T and k = ln(strike / forward), fitted by weighted least squares in total variance with weights 1 / IV^2 (so residuals approximate implied-volatility errors), with the wing slopes within Lee's bound and the minimum variance non-negative. One point per strike: the out-of-the-money contract, leaving out marks below 0.0005 BTC (five price ticks), which sit at the venue's price floor rather than on its smile. Every fit is checked for butterfly arbitrage (Gatheral's density condition across the fitted strikes) and calendar arbitrage (total variance falling with maturity at any strike) and repriced against the marks; failed checks are flagged, not hidden (Fitted Volatility Surface chart). Typical fit errors are 0.05 to 0.3 volatility points. Constant maturities interpolate total variance linearly in time between the two listed expiries around the target; no extrapolation, so 7 days needs an expiry within a week (Deribit lists daily ones). ATM is at the forward (k = 0); 25-delta strikes use Black-76 call deltas of 0.25 and 0.75 on the fitted smile. Source: our own ten-minute snapshots of Deribit's BTC option chain (each contract's mark implied volatility, Deribit's forward price for its expiry and its open interest), from 14 October 2026 13:00 UTC; no earlier values are reconstructed. Each period shows its last snapshot; the open period shows its latest snapshot as a labelled partial.