Finance

BAC Move Probability $50.81 +0.15 (+0.3%)

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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Optional: Options Contract Breakeven & Edge Analysis — test a specific strike and premium
Touch Probability (First Passage)
3.7%
Stock touched +5.0% ($53.35) at least once during 2 trading days.
Median first touch: Day 2 of 2
Expiration Close Probability
1.0%
Stock closed at or beyond +5.0% at the end of the 2-day window.
The Touch Multiple
3.80x
You are 3.8x more likely to hit your target during the window than holding until expiration.
1σ Expected Move (68.3%)
±2.2%
$49.67 — $51.95

Historical 2-Day Return Distribution

Frequency of rolling 2-day percentage returns over 520 historical windows (2024-09-23 to 2026-10-21). The colored bar indicates the win zone for +5.0%.

-17.8% to -16.1%: 1 occurrences (0.2%) -16.9% -16.1% to -14.3%: 0 occurrences (0.0%) -14.3% to -12.6%: 0 occurrences (0.0%) -12.6% to -10.9%: 0 occurrences (0.0%) -11.8% -10.9% to -9.2%: 1 occurrences (0.2%) -9.2% to -7.4%: 1 occurrences (0.2%) -7.4% to -5.7%: 2 occurrences (0.4%) -6.6% -5.7% to -4.0%: 14 occurrences (2.7%) -4.0% to -2.3%: 37 occurrences (7.1%) -2.3% to -0.6%: 116 occurrences (22.3%) -1.4% -0.6% to +1.2%: 171 occurrences (32.9%) +1.2% to +2.9%: 142 occurrences (27.3%) +2.9% to +4.6%: 26 occurrences (5.0%) 3.8% +4.6% to +6.3%: 6 occurrences (1.2%) +6.3% to +8.1%: 2 occurrences (0.4%) +8.1% to +9.8%: 1 occurrences (0.2%) 8.9%
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) 3.7% 1.0% Model-free reality across 520 historical 2-day windows.
Fat-Tail Adjusted (Cornish-Fisher) — 4.3% Adjusts normal bell curve for real-world skewness (-0.99) and kurtosis (8.55).
Standard Normal (Black-Scholes / GBM) 3.0% 1.5% Classic theoretical log-normal model with constant volatility (often underestimates tail risks).
Regime-Conditioned (Similar Volatility) 2.7% 1.0% Filters for historical windows that started with volatility similar to current 20-day HV (407 matching periods).

Underlying Volatility Profile

Volatility Metrics

  • 1-Year Annualized HV: 25.2%
  • Recent 20-Day HV: 22.1%
  • Parkinson Intraday Volatility: 21.3%
  • Vol Trend: Normal / Consistent

2-Day Return Quantiles

  • Median Return: +0.3%
  • Top 10% Move (90th percentile): +2.5%
  • Bottom 10% Move (10th percentile): -2.4%
  • Max Historical Gain (2d): +9.8%
  • Max Historical Loss (2d): -17.8%