# Monte Carlo Expected Move Distribution Monte Carlo Expected Move Distribution is an indicator on [Vela](https://vela.luxalgo.com/chart), our next-generation charting platform, written in Pine Script®. Runs up to 500 Geometric Brownian Motion simulations and condenses them into a forward histogram: median outcome, one-standard-deviation expected move, and low-probability tails. Targets, stops, and invalidation levels become probability decisions instead of guesses. For swing, intraday, and options-minded traders who plan in ranges. - Indicator in the LuxAlgo Library, by LuxAlgo, published Feb 19, 2026. - Access: free. - Concepts: [Monte Carlo Price Paths](https://www.luxalgo.com/library/concept/monte-carlo-price-paths/) (primary), [Probability Cones](https://www.luxalgo.com/library/concept/probability-cones/) - Open on Vela: https://vela.luxalgo.com/chart?pineScriptCodeId=cmpwn3ry5005avhsg1zxq4cfs - Page: https://www.luxalgo.com/library/indicator/monte-carlo-expected-move-distribution/ The **Monte Carlo Expected Move Distribution** swaps the single forecast line for an ensemble of [Monte Carlo price paths](https://www.luxalgo.com/library/concept/monte-carlo-price-paths/): up to 500 Geometric Brownian Motion simulations, seeded by historical log-volatility and an optional drift component, condensed into a vertical histogram at the end of your projection horizon. The result is an options-style expected move drawn on the chart: median, one-standard-deviation range, and improbable tails. ## How to Trade the Monte Carlo Expected Move Distribution? - **Median outcome (50th percentile)**: the statistically balanced reference given current volatility and drift. - **Colored 1-SD zone (16th–84th percentile)**: roughly 68% of simulated outcomes land here, home turf for conservative targets. - **Gray tails**: aggressive objectives with correspondingly low odds inside the window. - **Early ±1 SD touches**: reaching a dashed expected-move line early flags statistical overextension, context for mean reversion and trade management. - **Volatility-aware stops**: the lower expected move can guide long-trade stops, while the upper line serves shorts as an invalidation level. Match Projection Length to your holding period (a few bars for scalps, tens for swings) and enable drift only when you expect momentum to persist. The construction shares its geometry with [probability cones](https://www.luxalgo.com/library/concept/probability-cones/), rendered as a full distribution. ## Monte Carlo Expected Move Distribution Settings - **Simulations** (50–500): more paths produce smoother, more stable distributions. - **Projection Length**: forward bars used to compute the expected move. - **Volatility Lookback**: window for measuring historical log-return volatility. - **Include Trend (Drift)**: adds directional bias; disable for a mean-neutral random walk. - **Price Bins / Max Distribution Width**: vertical resolution and on-chart footprint of the histogram. ## Frequently Asked Questions ### What exactly is the expected move here? The band between the 16th and 84th percentiles of all simulated outcomes, the one-standard-deviation range that contains about 68% of cases under a normal distribution. It is a volatility statement, not a directional call. ### How does it differ from the Monte Carlo Mean Reversion Heatmap? The [Monte Carlo Mean Reversion Heatmap](https://www.luxalgo.com/library/indicator/monte-carlo-mean-reversion-heatmap/) scores the odds of price returning to a moving average; this indicator maps the entire forward range instead, which makes it the better fit for target-setting and range planning. ### How do I access the Monte Carlo Expected Move Distribution? The indicator is free from the LuxAlgo Library, and its page lets you run and backtest it in Quant, our coding agent. You can also copy the source code from this page and run it anywhere Pine Script® runs. ## Related indicators - [Monte Carlo Shuffled Projection](https://www.luxalgo.com/library/indicator/monte-carlo-shuffled-projection/) (Monte Carlo Price Paths): markdown at https://www.luxalgo.com/library/indicator/monte-carlo-shuffled-projection.md - [Monte Carlo Mean Reversion Heatmap](https://www.luxalgo.com/library/indicator/monte-carlo-mean-reversion-heatmap/) (Monte Carlo Price Paths): markdown at https://www.luxalgo.com/library/indicator/monte-carlo-mean-reversion-heatmap.md - [Predictive Monte Carlo Engine](https://www.luxalgo.com/library/indicator/predictive-monte-carlo-engine/) (Monte Carlo Price Paths): markdown at https://www.luxalgo.com/library/indicator/predictive-monte-carlo-engine.md - [Anchored Monte Carlo Shuffled Projection](https://www.luxalgo.com/library/indicator/anchored-monte-carlo-shuffled-projection/) (Monte Carlo Price Paths): markdown at https://www.luxalgo.com/library/indicator/anchored-monte-carlo-shuffled-projection.md - [Probability Grid](https://www.luxalgo.com/library/indicator/probability-grid/) (Probability Cones): markdown at https://www.luxalgo.com/library/indicator/probability-grid.md - [3D Opportunity Cone](https://www.luxalgo.com/library/indicator/3d-opportunity-cone/) (Probability Cones): markdown at https://www.luxalgo.com/library/indicator/3d-opportunity-cone.md - [Spline Quantile Regression Channel](https://www.luxalgo.com/library/indicator/spline-quantile-regression-channel/) (Statistics): markdown at https://www.luxalgo.com/library/indicator/spline-quantile-regression-channel.md - [Precision Market Entropy Heatmap](https://www.luxalgo.com/library/indicator/precision-market-entropy-heatmap/) (Statistics): markdown at https://www.luxalgo.com/library/indicator/precision-market-entropy-heatmap.md --- Source: https://www.luxalgo.com/library/indicator/monte-carlo-expected-move-distribution/ (LuxAlgo Library). Free to use with attribution: https://www.luxalgo.com/library/license/