Monte Carlo Simulation Bands

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Monte Carlo Simulation v2.4.2
Plots a one-bar-ahead price distribution band built from many simulated paths. The green band shows empirical percentiles of simulated final prices—these are distribution bounds, not a confidence interval of the mean.

What It Does
Simulates many one-bar price paths using a directional random walk with volatility scaling (uniform shocks, not Gaussian GBM).
Plots Mean Forecast, Median Forecast, and configurable percentile bounds (default 5th/95th).
Optional rolling HTF-days mean line (yellow) for trend context.
Optional labels and forward projection lines.
Alerts when the confirmed close breaks above or below the percentile band.

Non-Repainting & HTF Behavior (Fail-Closed)
All calculations are gated to confirmed bars only via explicit no_repaint_ok gate (barstate.isconfirmed).
If you select an HTF Resolution, the script uses a strict request.security(..., lookahead_off, gaps_off) pipeline.
If HTF data is unavailable, outputs are na—no silent fallback to chart timeframe.
A separate "HTF Alignment (lagged)" plot shows the prior HTF close (htf_price[1]) as visual proof of no look-ahead.

Volatility Source & Scaling
If "Use Historical Volatility" is enabled, volatility is estimated from log returns on the selected resolution (HTF if set, otherwise chart).
Annualization adapts to session type:
Equities: 6.5 hours/day, 252 trading days/year
Crypto: 24 hours/day, 365 days/year
Substeps increase path smoothness within the same one-bar horizon—they do not extend the forecast to multiple bars.

Key Inputs

• Prob Up / Prob Down — Must satisfy Prob Up + Prob Down ≤ 1.0. If violated, simulation is skipped and table shows "✗ PROB>1".
• # Simulations / # Substeps — Higher = smoother/more stable, but slower. Default 100×100 is a good balance.
• Lower/Upper Percentile — Define the band width (e.g., 5 and 95 for a 90% distribution band).
• Run On Last Bar Only — Performance mode (recommended). Skips historical computation; updates on each new confirmed bar.
• Resolution (HTF) — Leave blank for chart timeframe, or set to Weekly/Monthly for HTF-aligned simulation.
• Crypto 24/7 Session? — Enable for crypto markets to use correct annualization (365d, 24h).

How to Use (Quickstart)
Start with defaults and keep Run On Last Bar Only = true for speed.
Set Prob Up and Prob Down so their sum ≤ 1.0 (e.g., 0.5 + 0.5 = 1.0 for neutral).
Enable "Use Historical Volatility" and set a Volatility Lookback (e.g., 20 bars) for data-driven vol.
Set Resolution (HTF) if you want the model to run on higher timeframe data (e.g., 1W). Expect updates only when a new HTF interval starts.
Choose percentiles (e.g., 5 and 95) to define your distribution band width.
Enable alerts for "Price Above Upper Percentile" or "Price Below Lower Percentile" to get notified of breakouts.

Limitations & Disclosures

• Forecast horizon is one bar only. Substeps do not create a multi-bar forecast.
  
• Model uses uniform shocks with direction chosen from Prob Up/Down. This is not Geometric Brownian Motion (GBM) and is not calibrated to any option-implied distribution.
  
• Bounds are percentiles of final simulated prices, not a statistical confidence interval of the mean.
  
• HTF mode updates at the start of a new HTF interval (first chart bar where the HTF timestamp changes), so the band appears "step-like" in realtime.
  
• Historical volatility requires enough bars for the selected lookback; until then, values may be na.
  
• Performance depends on Sims × Substeps; extreme settings (e.g., 500×500) can be slow.
  
• This indicator does not predict direction—it shows a probabilistic range based on your inputs.
  

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Versionshinweise

Fixed an error in referencing too many historical bars