Finance

BILL Move Probability $49.03 -0.05 (-0.1%)

Real historical back-data analysis: evaluates rolling trading-day windows to determine the probability of a stock touching or closing at your target move.

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Touch Probability (First Passage)
9.8%
Stock touched +5.0% ($51.48) at least once during 1 trading days.
Median first touch: Day 1 of 1
Expiration Close Probability
6.0%
Stock closed at or beyond +5.0% at the end of the 1-day window.
The Touch Multiple
1.65x
You are 1.6x more likely to hit your target during the window than holding until expiration.
1σ Expected Move (68.3%)
±4.0%
$47.08 — $50.98

Historical 1-Day Return Distribution

Frequency of rolling 1-day percentage returns over 521 historical windows (2024-09-23 to 2026-10-21). The colored bar indicates the win zone for +5.0%.

-35.6% to -31.1%: 1 occurrences (0.2%) -33.3% -31.1% to -26.6%: 0 occurrences (0.0%) -26.6% to -22.0%: 0 occurrences (0.0%) -22.0% to -17.5%: 0 occurrences (0.0%) -19.8% -17.5% to -13.0%: 0 occurrences (0.0%) -13.0% to -8.4%: 4 occurrences (0.8%) -8.4% to -3.9%: 40 occurrences (7.7%) -6.2% -3.9% to +0.6%: 265 occurrences (50.9%) +0.6% to +5.1%: 183 occurrences (35.1%) +5.1% to +9.7%: 20 occurrences (3.8%) 7.4% +9.7% to +14.2%: 4 occurrences (0.8%) +14.2% to +18.7%: 3 occurrences (0.6%) +18.7% to +23.3%: 0 occurrences (0.0%) 21.0% +23.3% to +27.8%: 0 occurrences (0.0%) +27.8% to +32.3%: 0 occurrences (0.0%) +32.3% to +36.8%: 1 occurrences (0.2%) 34.6%
Historical returns Target move zone (+5.0%+) Target threshold bin

Probability Breakdown: Empirical vs. Theoretical Models

Comparing actual market back-data against Black-Scholes and Fat-Tail adjustments.

Model / Methodology Touch Probability Expiration Close Probability What It Tells You
Empirical Back-Data (Actual History) 9.8% 6.0% Model-free reality across 521 historical 1-day windows.
Fat-Tail Adjusted (Cornish-Fisher) — 0.0% Adjusts normal bell curve for real-world skewness (-1.31) and kurtosis (36.02).
Standard Normal (Black-Scholes / GBM) 22.0% 11.0% Classic theoretical log-normal model with constant volatility (often underestimates tail risks).
Regime-Conditioned (Similar Volatility) 10.6% 7.0% Filters for historical windows that started with volatility similar to current 20-day HV (359 matching periods).

Underlying Volatility Profile

Volatility Metrics

  • 1-Year Annualized HV: 63.2%
  • Recent 20-Day HV: 46.4%
  • Parkinson Intraday Volatility: 41.2%
  • Vol Trend: Compressed (-27% vs baseline)

1-Day Return Quantiles

  • Median Return: +0.0%
  • Top 10% Move (90th percentile): +3.4%
  • Bottom 10% Move (10th percentile): -3.5%
  • Max Historical Gain (1d): +36.8%
  • Max Historical Loss (1d): -35.6%