Finance

MUU Move Probability $24.37 +1.46 (+6.4%)

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

← Back to MUU Options chain →
Optional: Options Contract Breakeven & Edge Analysis — test a specific strike and premium
Touch Probability (First Passage)
41.6%
Stock touched +5.0% ($25.59) at least once during 1 trading days.
Median first touch: Day 1 of 1
Expiration Close Probability
29.6%
Stock closed at or beyond +5.0% at the end of the 1-day window.
The Touch Multiple
1.40x
You are 1.4x more likely to hit your target during the window than holding until expiration.
1σ Expected Move (68.3%)
±13.5%
$21.08 — $27.66

Historical 1-Day Return Distribution

Frequency of rolling 1-day percentage returns over 510 historical windows (2024-10-10 to 2026-10-23). The colored bar indicates the win zone for +5.0%.

-33.8% to +18.0%: 492 occurrences (96.5%) -7.9% +18.0% to +69.7%: 16 occurrences (3.1%) +69.7% to +121.4%: 0 occurrences (0.0%) +121.4% to +173.1%: 1 occurrences (0.2%) 147.3% +173.1% to +224.8%: 0 occurrences (0.0%) +224.8% to +276.6%: 0 occurrences (0.0%) +276.6% to +328.3%: 0 occurrences (0.0%) 302.4% +328.3% to +380.0%: 0 occurrences (0.0%) +380.0% to +431.7%: 0 occurrences (0.0%) +431.7% to +483.4%: 0 occurrences (0.0%) 457.6% +483.4% to +535.2%: 0 occurrences (0.0%) +535.2% to +586.9%: 0 occurrences (0.0%) +586.9% to +638.6%: 0 occurrences (0.0%) 612.7% +638.6% to +690.3%: 0 occurrences (0.0%) +690.3% to +742.1%: 0 occurrences (0.0%) +742.1% to +793.8%: 1 occurrences (0.2%) 767.9%
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) 41.6% 29.6% Model-free reality across 510 historical 1-day windows.
Fat-Tail Adjusted (Cornish-Fisher) — 0.0% Adjusts normal bell curve for real-world skewness (8.51) and kurtosis (133.03).
Standard Normal (Black-Scholes / GBM) 71.8% 35.9% Classic theoretical log-normal model with constant volatility (often underestimates tail risks).
Regime-Conditioned (Similar Volatility) 40.7% 30.0% Filters for historical windows that started with volatility similar to current 20-day HV (253 matching periods).

Underlying Volatility Profile

Volatility Metrics

  • 1-Year Annualized HV: 214.4%
  • Recent 20-Day HV: 102.8%
  • Parkinson Intraday Volatility: 89.8%
  • Vol Trend: Compressed (-52% vs baseline)

1-Day Return Quantiles

  • Median Return: +0.2%
  • Top 10% Move (90th percentile): +10.9%
  • Bottom 10% Move (10th percentile): -8.5%
  • Max Historical Gain (1d): +793.8%
  • Max Historical Loss (1d): -33.8%