Finance

MRK Move Probability $149.88 +1.64 (+1.1%)

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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Optional: Options Contract Breakeven & Edge Analysis — test a specific strike and premium
Touch Probability (First Passage)
1.9%
Stock touched +5.0% ($157.37) at least once during 1 trading days.
Median first touch: Day 1 of 1
Expiration Close Probability
1.2%
Stock closed at or beyond +5.0% at the end of the 1-day window.
The Touch Multiple
1.67x
You are 1.7x more likely to hit your target during the window than holding until expiration.
1σ Expected Move (68.3%)
±1.8%
$147.16 — $152.60

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%.

-9.1% to -7.8%: 1 occurrences (0.2%) -8.5% -7.8% to -6.4%: 0 occurrences (0.0%) -6.4% to -5.1%: 2 occurrences (0.4%) -5.1% to -3.7%: 7 occurrences (1.3%) -4.4% -3.7% to -2.3%: 23 occurrences (4.4%) -2.3% to -1.0%: 97 occurrences (18.6%) -1.0% to +0.4%: 178 occurrences (34.2%) -0.3% +0.4% to +1.7%: 141 occurrences (27.1%) +1.7% to +3.1%: 49 occurrences (9.4%) +3.1% to +4.4%: 15 occurrences (2.9%) 3.8% +4.4% to +5.8%: 4 occurrences (0.8%) +5.8% to +7.2%: 2 occurrences (0.4%) +7.2% to +8.5%: 1 occurrences (0.2%) 7.8% +8.5% to +9.9%: 0 occurrences (0.0%) +9.9% to +11.2%: 0 occurrences (0.0%) +11.2% to +12.6%: 1 occurrences (0.2%) 11.9%
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) 1.9% 1.2% Model-free reality across 521 historical 1-day windows.
Fat-Tail Adjusted (Cornish-Fisher) — 55.6% Adjusts normal bell curve for real-world skewness (0.39) and kurtosis (5.35).
Standard Normal (Black-Scholes / GBM) 0.7% 0.4% Classic theoretical log-normal model with constant volatility (often underestimates tail risks).
Regime-Conditioned (Similar Volatility) 2.1% 1.0% Filters for historical windows that started with volatility similar to current 20-day HV (387 matching periods).

Underlying Volatility Profile

Volatility Metrics

  • 1-Year Annualized HV: 28.8%
  • Recent 20-Day HV: 29.4%
  • Parkinson Intraday Volatility: 23.7%
  • Vol Trend: Normal / Consistent

1-Day Return Quantiles

  • Median Return: +0.0%
  • Top 10% Move (90th percentile): +2.0%
  • Bottom 10% Move (10th percentile): -2.0%
  • Max Historical Gain (1d): +12.6%
  • Max Historical Loss (1d): -9.1%