# Probability Cones A Statistics concept (Simulation) in the LuxAlgo Library, with 5 indicator implementations. ## What are Probability Cones? Probability cones are forward-projected envelopes, anchored at the current price, an entry, or an event, that show where price is statistically expected to remain at chosen confidence levels. The width scales with a volatility input, either realized volatility from recent history or implied volatility from options, and grows with the square root of elapsed time, because under independent returns the variance of the cumulative move accumulates linearly with time. Confidence labels come from a distributional assumption. Under a normal approximation, an envelope of one standard deviation covers roughly 68 percent of outcomes and two standard deviations roughly 95 percent; cones can also be built empirically as percentile bands over [Monte Carlo price paths](https://www.luxalgo.com/library/concept/monte-carlo-price-paths/). Real returns are fatter-tailed than normal, so actual breach rates run higher than the labels suggest, and a cone edge is a statistical boundary, not support or resistance. No single author owns the construction. The square-root-of-time core descends from Louis Bachelier's 1900 random-walk thesis and became standard machinery with the lognormal Black-Scholes framework in 1973. Options platforms later turned the math into a chart object: the cone is the visual form of the 'expected move' quoted around earnings and expirations. The construction is simple enough to audit: annualized volatility is rescaled to the horizon (sigma times the square root of time), multiplied by a [z-score](https://www.luxalgo.com/library/concept/z-score/) for the chosen confidence, and projected from the anchor, with drift usually ignored because expected return is tiny next to dispersion. Where normality fits badly, empirical variants substitute percentile bands from the asset's own [distribution of returns](https://www.luxalgo.com/library/concept/distribution-of-returns-profiling/), and filter models such as the [Kalman filter](https://www.luxalgo.com/library/concept/kalman-filter/) supply a forecast variance of their own. The cone's value is honesty about uncertainty: a widening set of outcomes instead of a point prediction. ## How to set up a probability cone on a chart Cones are configured rather than spotted; settings decide whether the envelope means anything. 1. Pick the anchor: the current bar for a general forecast, your entry for trade planning, or a scheduled event like an earnings date. 2. Choose the volatility input: historical volatility over a lookback comparable to the horizon, or implied volatility when the horizon matches an expiry. 3. Set the confidence levels: one and two standard deviations are conventional, while percentile bands avoid the normality assumption where tools support empirical cones. 4. Read the width at your horizon, not the chart's edge: the band prices on your intended exit date are the expected-move estimate that matters. 5. Track the realized path against the cone: riding an outer band or escaping early means volatility is running hotter than assumed and the plan is stale. ## How traders use it - As an expected-move frame for options horizons: comparing a target against the cone implied by option pricing shows whether the trade needs an outsized move by the market's own estimate. - As a realism check on stops and targets: a target sitting outside the cone for the trade's intended horizon is, under the model, a low-probability outcome, which argues for resizing the trade or allowing more time. - As post-entry context: price hugging or escaping the cone flags a move that is large relative to the volatility regime the cone assumed, often a prompt to reassess the position. - As a sizing translator: the cone turns a volatility estimate into concrete prices, so size can be set such that an ordinary one-standard-deviation excursion against the position stays within the risk budget. - As a model check: overlaying a normal-assumption cone with an empirical one from the same history makes fat tails visible, and positive [autocorrelation](https://www.luxalgo.com/library/concept/autocorrelation/) in returns shows up as breach rates running above the labels. - As a regime dashboard: comparing the current cone's width against past anchors, normalized with a [percentile rank](https://www.luxalgo.com/library/concept/percentile-rank/), shows whether present uncertainty is historically stretched or compressed. ## Probability Cones vs related concepts - **Monte Carlo Price Paths** (https://www.luxalgo.com/library/concept/monte-carlo-price-paths/): A cone is a summary; a simulation is the raw material. Monte Carlo methods generate thousands of hypothetical paths, and percentile bands across them form an empirical cone. The parametric version skips simulation by assuming a distribution up front. - **Linear Regression** (https://www.luxalgo.com/library/concept/linear-regression/): A linear regression channel is fitted to past prices, describing a trend that already happened with parallel bands of constant width. A cone is anchored at a point and projects forward, widening with time. One is descriptive, the other a forecast envelope. - **Exponential Smoothing Forecasts** (https://www.luxalgo.com/library/concept/exponential-smoothing-forecasts/): Smoothing models produce a central point forecast, with uncertainty added as prediction intervals. A probability cone usually skips the point forecast: it centers on the anchor and models dispersion alone. One commits to a path, the other brackets the possibilities. ## FAQ ### What does a 95 percent probability cone actually mean? It means that under the model's assumptions (the chosen volatility, roughly normal returns, no regime change) about 95 percent of outcomes stay inside the envelope through the horizon. It is a statement about the model, not a promise from the market: fat tails and volatility shifts push real breach rates above the label, and touching the edge is not a trade signal by itself. ### Should probability cones use implied or historical volatility? They answer different questions. Implied volatility embeds the market's forward-looking pricing, including known events, so options traders usually prefer it for horizons to expiry. Historical volatility describes the recent past and works on anything without an options market. Neither is correct by default; when the two disagree sharply, that gap itself is information about priced-in event risk. ### Why do probability cones widen with the square root of time? Because uncertainty compounds. Under roughly independent returns the variance of the cumulative move grows linearly with time, so the standard deviation setting the cone's width grows with its square root: the envelope flares quickly at first, then ever more gradually. ### Are probability cones the same as Bollinger Bands? No. Bollinger Bands trail the market, wrapping a moving average of past prices in past volatility, updating bar by bar. A cone is anchored at one moment and projects forward without touching future data. Bands describe where price has been; cones estimate where it may go. ### Can a probability cone predict direction? No. Most cones are symmetric around their anchor, since drift is negligible over trading horizons: they bound the plausible size of a move, not its sign. Direction has to come from elsewhere; the cone then prices how far that opinion can reasonably travel. ### What lookback should the historical volatility input use? There is no single right answer. A defensible default matches the lookback to the horizon: a one-month projection draws on one to three months of returns. Short lookbacks adapt quickly but whipsaw; long ones are stable but slow to register regime change. ## Implementations in the Library - Probability Grid (LuxAlgo): https://www.luxalgo.com/library/indicator/probability-grid/ - 3D Opportunity Cone (LuxAlgo): https://www.luxalgo.com/library/indicator/3d-opportunity-cone/ - Predictive Monte Carlo Engine (LuxAlgo): https://www.luxalgo.com/library/indicator/predictive-monte-carlo-engine/ - Monte Carlo Mean Reversion Heatmap (LuxAlgo): https://www.luxalgo.com/library/indicator/monte-carlo-mean-reversion-heatmap/ - Monte Carlo Expected Move Distribution (LuxAlgo): https://www.luxalgo.com/library/indicator/monte-carlo-expected-move-distribution/ ## Related concepts - Monte Carlo Price Paths: https://www.luxalgo.com/library/concept/monte-carlo-price-paths/ - Resampling Tests: https://www.luxalgo.com/library/concept/resampling-tests/ - Random-entry Baselines: https://www.luxalgo.com/library/concept/random-entry-baselines/ --- Source: https://www.luxalgo.com/library/concept/probability-cones/ (LuxAlgo Library, the encyclopedia of trading & technical analysis). Free to use with attribution: https://www.luxalgo.com/library/license/