MONTECARLO — Indicators and Strategies

Seasonality Monte Carlo Forecaster [BackQuant]Seasonality Monte Carlo Forecaster Plain-English overview This tool projects a cone of plausible future prices by combining two ideas that traders already use intuitively: seasonality and uncertainty. It watches how your market typically behaves around this calendar date, turns that seasonal tendency into a small daily “drift,” then runs many randomized price paths forward to estimate where price could land tomorrow, next week, or a month from now. The result is a probability cone with a clear expected path, plus optional overlays that show how past years tended to move from this point on the calendar. It is a planning tool, not a crystal ball: the goal is to quantify ranges and odds so you can size, place stops, set targets, and time entries with more realism. What Monte Carlo is and why quants rely on it • Definition . Monte Carlo simulation is a way to answer “what might happen next?” when there is randomness in the system. Instead of producing a single forecast, it generates thousands of alternate futures by repeatedly sampling random shocks and adding them to a model of how prices evolve. • Why it is used . Markets are noisy. A single point forecast hides risk. Monte Carlo gives a distribution of outcomes so you can reason in probabilities: the median path, the 68% band, the 95% band, tail risks, and the chance of hitting a specific level within a horizon. • Core strengths in quant finance . – Path-dependent questions : “What is the probability we touch a stop before a target?” “What is the expected drawdown on the way to my objective?” – Pricing and risk : Useful for path-dependent options, Value-at-Risk (VaR), expected shortfall (CVaR), stress paths, and scenario analysis when closed-form formulas are unrealistic. – Planning under uncertainty : Portfolio construction and rebalancing rules can be tested against a cloud of plausible futures rather than a single guess. • Why it fits trading workflows . It turns gut feel like “seasonality is supportive here” into quantitative ranges: “median path suggests +X% with a 68% band of ±Y%; stop at Z has only ~16% odds of being tagged in N days.” How this indicator builds its probability cone 1) Seasonal pattern discovery The script builds two day-of-year maps as new data arrives: • A return map where each calendar day stores an exponentially smoothed average of that day’s log return (yesterday→today). The smoothing (90% old, 10% new) behaves like an EWMA, letting older seasons matter while adapting to new information. • A volatility map that tracks the typical absolute return for the same calendar day. It calculates the day-of-year carefully (with leap-year adjustment) and indexes into a 365-slot seasonal array so “March 18” is compared with past March 18ths. This becomes the seasonal bias that gently nudges simulations up or down on each forecast day. 2) Choice of randomness engine You can pick how the future shocks are generated: • Daily mode uses a Gaussian draw with the seasonal bias as the mean and a volatility that comes from realized returns, scaled down to avoid over-fitting. It relies on the Box–Muller transform internally to turn two uniform random numbers into one normal shock. • Weekly mode uses bootstrap sampling from the seasonal return history (resampling actual historical daily drifts and then blending in a fraction of the seasonal bias). Bootstrapping is robust when the empirical distribution has asymmetry or fatter tails than a normal distribution. Both modes seed their random draws deterministically per path and day, which makes plots reproducible bar-to-bar and avoids flickering bands. 3) Volatility scaling to current conditions Markets do not always live in average volatility. The engine computes a simple volatility factor from ATR(20)/price and scales the simulated shocks up or down within sensible bounds (clamped between 0.5× and 2.0×). When the current regime is quiet, the cone narrows; when ranges expand, the cone widens. This prevents the classic mistake of projecting calm markets into a storm or vice versa. 4) Many futures, summarized by percentiles The model generates a matrix of price paths (capped at 100 runs for performance inside TradingView), each path stepping forward for your selected horizon. For each forecast day it sorts the simulated prices and pulls key percentiles: • 5th and 95th → approximate 95% band (outer cone). • 16th and 84th → approximate 68% band (inner cone). • 50th → the median or “expected path.” These are drawn as polylines so you can immediately see central tendency and dispersion. 5) A historical overlay (optional) Turn on the overlay to sketch a dotted path of what a purely seasonal projection would look like for the next ~30 days using only the return map, no randomness. This is not a forecast; it is a visual reminder of the seasonal drift you are biasing toward. Inputs you control and how to think about them Monte Carlo Simulation • Price Series for Calculation . The source series, typically close. • Enable Probability Forecasts . Master switch for simulation and drawing. • Simulation Iterations . Requested number of paths to run. Internally capped at 100 to protect performance, which is generally enough to estimate the percentiles for a trading chart. If you need ultra-smooth bands, shorten the horizon. • Forecast Days Ahead . The length of the cone. Longer horizons dilute seasonal signal and widen uncertainty. • Probability Bands . Draw all bands, just 95%, just 68%, or a custom level (display logic remains 68/95 internally; the custom number is for labeling and color choice). • Pattern Resolution . Daily leans on day-of-year effects like “turn-of-month” or holiday patterns. Weekly biases toward day-of-week tendencies and bootstraps from history. • Volatility Scaling . On by default so the cone respects today’s range context. Plotting & UI • Probability Cone . Plots the outer and inner percentile envelopes. • Expected Path . Plots the median line through the cone. • Historical Overlay . Dotted seasonal-only projection for context. • Band Transparency/Colors . Customize primary (outer) and secondary (inner) band colors and the mean path color. Use higher transparency for cleaner charts. What appears on your chart • A cone starting at the most recent bar, fanning outward. The outer lines are the ~95% band; the inner lines are the ~68% band. • A median path (default blue) running through the center of the cone. • An info panel on the final historical bar that summarizes simulation count, forecast days, number of seasonal patterns learned, the current day-of-year, expected percentage return to the median, and the approximate 95% half-range in percent. • Optional historical seasonal path drawn as dotted segments for the next 30 bars. How to use it in trading 1) Position sizing and stop logic The cone translates “volatility plus seasonality” into distances. • Put stops outside the inner band if you want only ~16% odds of a stop-out due to noise before your thesis can play. • Size positions so that a test of the inner band is survivable and a test of the outer band is rare but acceptable. • If your target sits inside the 68% band at your horizon, the payoff is likely modest; outside the 68% but inside the 95% can justify “one-good-push” trades; beyond the 95% band is a low-probability flyer—consider scaling plans or optionality. 2) Entry timing with seasonal bias When the median path slopes up from this calendar date and the cone is relatively narrow, a pullback toward the lower inner band can be a high-quality entry with a tight invalidation. If the median slopes down, fade rallies toward the upper band or step aside if it clashes with your system. 3) Target selection Project your time horizon to N bars ahead, then pick targets around the median or the opposite inner band depending on your style. You can also anchor dynamic take-profits to the moving median as new bars arrive. 4) Scenario planning & “what-ifs” Before events, glance at the cone: if the 95% band already spans a huge range, trade smaller, expect whips, and avoid placing stops at obvious band edges. If the cone is unusually tight, consider breakout tactics and be ready to add if volatility expands beyond the inner band with follow-through. 5) Options and vol tactics • When the cone is tight : Prefer long gamma structures (debit spreads) only if you expect a regime shift; otherwise premium selling may dominate. • When the cone is wide : Debit structures benefit from range; credit spreads need wider wings or smaller size. Align with your separate IV metrics. Reading the probability cone like a pro • Cone slope = seasonal drift. Upward slope means the calendar has historically favored positive drift from this date, downward slope the opposite. • Cone width = regime volatility. A widening fan tells you that uncertainty grows fast; a narrow cone says the market typically stays contained. • Mean vs. price gap . If spot trades well above the median path and the upper band, mean-reversion risk is high. If spot presses the lower inner band in an up-sloping cone, you are in the “buy fear” zone. • Touches and pierces . Touching the inner band is common noise; piercing it with momentum signals potential regime change; the outer band should be rare and often brings snap-backs unless there is a structural catalyst. Methodological notes (what the code actually does) • Log returns are used for additivity and better statistical behavior: sim_ret is applied via exp(sim_ret) to evolve price. • Seasonal arrays are updated online with EWMA (90/10) so the model keeps learning as each bar arrives. • Leap years are handled; indexing still normalizes into a 365-slot map so the seasonal pattern remains stable. • Gaussian engine (Daily mode) centers shocks on the seasonal bias with a conservative standard deviation. • Bootstrap engine (Weekly mode) resamples from observed seasonal returns and adds a fraction of the bias, which captures skew and fat tails better. • Volatility adjustment multiplies each daily shock by a factor derived from ATR(20)/price, clamped between 0.5 and 2.0 to avoid extreme cones. • Performance guardrails : simulations are capped at 100 paths; the probability cone uses polylines (no heavy fills) and only draws on the last confirmed bar to keep charts responsive. • Prerequisite data : at least ~30 seasonal entries are required before the model will draw a cone; otherwise it waits for more history. Strengths and limitations • Strengths : – Probabilistic thinking replaces single-point guessing. – Seasonality adds a small but meaningful directional bias that many markets exhibit. – Volatility scaling adapts to the current regime so the cone stays realistic. • Limitations : – Seasonality can break around structural changes, policy shifts, or one-off events. – The number of paths is performance-limited; percentile estimates are good for trading, not for academic precision. – The model assumes tomorrow’s randomness resembles recent randomness; if regime shifts violently, the cone will lag until the EWMA adapts. – Holidays and missing sessions can thin the seasonal sample for some assets; be cautious with very short histories. Tuning guide • Horizon : 10–20 bars for tactical trades; 30+ for swing planning when you care more about broad ranges than precise targets. • Iterations : The default 100 is enough for stable 5/16/50/84/95 percentiles. If you crave smoother lines, shorten the horizon or run on higher timeframes. • Daily vs. Weekly : Daily for equities and crypto where month-end and turn-of-month effects matter; Weekly for futures and FX where day-of-week behavior is strong. • Volatility scaling : Keep it on. Turn off only when you intentionally want a “pure seasonality” cone unaffected by current turbulence. Workflow examples • Swing continuation : Cone slopes up, price pulls into the lower inner band, your system fires. Enter near the band, stop just outside the outer line for the next 3–5 bars, target near the median or the opposite inner band. • Fade extremes : Cone is flat or down, price gaps to the upper outer band on news, then stalls. Favor mean-reversion toward the median, size small if volatility scaling is elevated. • Event play : Before CPI or earnings on a proxy index, check cone width. If the inner band is already wide, cut size or prefer options structures that benefit from range. Good habits • Pair the cone with your entry engine (breakout, pullback, order flow). Let Monte Carlo do range math; let your system do signal quality. • Do not anchor blindly to the median; recalc after each bar. When the cone’s slope flips or width jumps, the plan should adapt. • Validate seasonality for your symbol and timeframe; not every market has strong calendar effects. Summary The Seasonality Monte Carlo Forecaster wraps institutional risk planning into a single overlay: a data-driven seasonal drift, realistic volatility scaling, and a probabilistic cone that answers “where could we be, with what odds?” within your trading horizon. Use it to place stops where randomness is less likely to take you out, to set targets aligned with realistic travel, and to size positions with confidence born from distributions rather than hunches. It will not predict the future, but it will keep your decisions anchored to probabilities—the language markets actually speak.

Monte Carlo (Polyline Traceback) [Kioseff Trading]Hello! This script "Monte Carlo (Polyline Traceback) " performs a Monte Carlo simulation using polylines! By using polylines, and tracing back the initial simulation to its origin point, we can better replicate the ideal output of a Monte Carlo simulation! Such as: The image above shows the output of a simulation (image sourced outside TV). With this script, and polyline capabilities, we can come quite close on TradingView. The image above shows the indicator in action! Not bad considering the ideal output. Of course, the script is quite heavy and tries its best to circumvent limitations :D You might run into load time errors, in which case you might try applying the built-in setting "Force Script Load". This setting will cut-off the visuals for some simulations, but has a higher chance of passing load-time limitations! As shown in the image above, you can select to only show worst-case and best-case simulations. Using this option will reduce chart lag and improve load times. Features Monte Carlo Simulation: Performs Monte Carlo simulation to generate multiple future paths. Asset Price: Can simulate future asset prices based on historical log returns. Statistical Methods: Offers two simulation methods—Gaussian (Normal) distribution and Bootstrapping. Adjustable Parameters: Offers numerous user-adjustable settings like number of simulations, forecast length, and more. Historical Data Points: Option to specify the amount of historical data to be used in the simulation (price). Best/Worst Case: Allows you to show only the best case / worst case outcome (range) for all simulations! Thank you!

Anchored Monte Carlo Shuffled Projection [LuxAlgo]The Anchored Monte Carlo Shuffled Projection tool randomly simulates future price points based on historical bar movements made before a user-anchored point in time. By anchoring our data and projections to a single point in time, users can better understand and reflect on how the price played out while taking into consideration our random simulations. 🔶 USAGE After selecting the indicator to apply to the chart, you will be prompted to "Set the Anchor Point". Do so by clicking on the desired location on your chart, only time is used as the anchor point. Note: To select a new anchor point when applied to the chart, click on the 'More' dropdown next to the indicator status bar (○○○), then select "Reset points...". Alternate Method: You are also able to click and drag the vertical line that displays on the anchor point bar when the indicator is highlighted. By randomly simulating bar movements, a range is developed of potential price action which could be utilized to locate future price development as well as potential support/resistance levels. Performing numerous simulations and taking the average at each step will converge toward the result highlighted by the "Average Line", and can point out where the price might develop, assuming the trend and amount of volatility persist. Current closing price + Sum of changes in the calculation window This constraint will cause the simulations always to display an endpoint consistent with the current lookback's slope. While this may be helpful to some traders, this indicator includes an option to produce a less biased range, as seen below: 🔶 DETAILS The Anchored Monte Carlo Shuffled Projection tool creates simulations based on prices within a user-set lookback window originating at the specified anchor point. Simulations are done as follows: Collect each bar's price changes in the user-set window. Randomize the order of each change in the window. Project the cumulative sum of the shuffled changes from the current closing price. Collect data on each point along the way. This is the process for the Default calculation; for the 'Randomize Direction' calculation, when added onto the front for every other change, the value is inverted, creating the randomized endpoints for each simulation. The script contains each simulation's data for that bar, with a maximum of 1000 simulations. To get a glimpse behind the scenes, each simulation (up to 99) can be viewed using the 'Visualize Simulations' Options, as seen below. Because the script holds the full simulation data, the script can also calculate this data, such as standard deviations. In this script the Standard deviation lines are the average of all standard deviations across the vertical data groups, this provides a singular value that can be displayed a distance away from the simulation center line. 🔶 SETTINGS Lookback: Sets the number of Bars to include in calculations. Simulation Count: Sets the number of randomized simulations to calculate. (Max 1000) Randomize Direction: See Details Above. Creates a more 'Normalized' Distribution Visualize Simulations: See Details Above. Turns on Visualizations, and colors are randomly generated. Visualized max does not cap the calculated max. If 1000 simulations are used, the data will be from 1000 simulations, however, only the last 99 simulations will be visualized. 🔹 Standard Deviations Standard Deviation Multiplier: Sets the multiplier to use for the Standard Deviation distance away from the center line. 🔹 Style Extend Lines: Extends the Simulated Value Lines into the future for further reference and analysis.

Monte Carlo Shuffled Projection [LuxAlgo]The Monte Carlo Shuffled Projection tool randomly simulates future price points based on historical bar movements made within a user-selected window. The tool shows potential paths price might take in the future, as well as highlighting potential support/resistance levels. Note that simulations and their resulting elements are subject to slight changes over time. 🔶 USAGE By randomly simulating bar movements, a range is developed of potential price action which could be utilized to locate future price development as well as potential support/resistance levels. Performing a large number of simulations and taking the average at each step will converge toward the result highlighted by the "Average Line", and can point out where the price might develop assuming the trend and amount of volatility persist. Current closing price + Sum of changes in the calculation window) This constraint will cause the simulations to always display an endpoint consistent with the current lookback's slope. While this may be helpful to some traders, this indicator includes an option to produce a less biased range as seen below: 🔶 DETAILS The Monte Carlo Shuffled Projection tool creates simulations based on the most recent prices within a user-set window. Simulations are done as follows: Collect each bar's price changes in the user-set window. Randomize the order of each change in the window. Project the cumulative sum of the shuffled changes from the current closing price. Collect data on each point along the way. This is the process for the Default calculation, for the 'Randomize Direction' calculation, when added onto the front for every other change, the value is inverted, creating the randomized endpoints for each simulation. The script contains each simulation's data for that bar with a maximum of 1000 simulations. To get a glimpse behind the scenes each simulation (up to 99) can be viewed using the 'Visualize Simulations' Options as seen below. Because the script holds the full simulation data, the script can also do calculations on this data, such as calculating standard deviations. In this script the Standard deviation lines are the average of all standard deviations across the vertical data groups, this provides a singular value that can be displayed a distance away from the simulation center line. 🔶 SETTINGS Color and Toggle Options are Provided throughout. Lookback: Sets the number of Bars to include in calculations. Simulation Count: Sets the number of randomized simulations to calculate. (Max 1000) Randomize Direction: See Details Above. Creates a more 'Normalized' Distribution Visualize Simulations: See Details Above. Turns on Visualizations, and colors are randomly generated. Visualized max does not cap the calculated max. If 1000 simulations are used, the data will be from 1000 simulations, however only the last 99 simulations will be visualized. Standard Deviation Multiplier: Sets the multiplier to use for the Standard Deviation distance away from the center line.

Monte Carlo Simulation - Your Strategy [Kioseff Trading]Hello! This script “Monte Carlo Simulation - Your Strategy” uses Monte Carlo simulations for your inputted strategy returns or the asset on your chart! Features Monte Carlo Simulation: Performs Monte Carlo simulation to generate multiple future paths. Asset Price or Strategy: Can simulate either future asset prices based on historical log returns or a specific trading strategy's future performance. User-Defined Input: Allows you to input your own historical returns for simulation. Statistical Methods: Offers two simulation methods—Gaussian (Normal) distribution and Bootstrapping. Graphical Display: Provides options for graphical representation, including line plots and histograms. Cumulative Probability Target: Enables setting a user-defined cumulative probability target to quantify simulation results. Adjustable Parameters: Offers numerous user-adjustable settings like number of simulations, forecast length, and more. Historical Data Points: Option to specify the amount of historical data to be used in the simulation (price). Custom Binning: Allows you to select the binning method for histograms, with options like Sturges, Rice, and Square Root. Best/Worst Case: Allows you to show only the best case / worst case outcome (range) for all simulations! Scatterplot: allows you to show up to 1000 potential outcomes for a specified trade number (or bars forward price endpoint) using a scatter plot. The image above shows the primary components of the indicator! The image above shows the best/worst case outcome feature in action! The image above shows a "fun feature" where 1000 simulated end points for a 15-bar price trajectory are shown as a scatter plot! How To Perform a Monte Carlo Simulation On Your Strategy Really, you can input any data into the indicator it will perform a Monte Carlo Simulation on it :D The following instructions show how to export your strategy results from TradingView to an Excel File, copy the data, and input it into the indicator. However , you are not limited to following this method! Wherever your strategy results are stored, simply copy and paste them into the indicator text area in the settings and simulations will begin. Returns Should Follow This Format 1 3 -3 2 -5 The numbers are presented as a single column. No commas or separators used. The numbers above are in sequential order. A return of "1" for the first trade and a return of "-5" for the last trade. Your strategy returns will likely be in sequential order already so don't worry too much about this (: How To Perform a Monte Carlo Simulation On Your TradingView Strategy With Excel Data Export your strategy returns to an excel file using TradingView Navigate to your downloads folder to column G "Profit" Click the column and press CTRL + SPACE to highlight the entire column Press CTRL + C to copy the entire column Open this indicator's settings and paste the returns into the text area The image above illustrates the process! Notes on Inputting Returns *Must input your returns without a separate as a vertical list *The initial text area can only hold so many return values. If your list of trades is large you can input additional returns into two additional text areas at the bottom of the indicator settings. That should be it; thank you for checking this out!

Drift Study (Inspired by Monte Carlo Simulations with BM) [KL]Inspired by the Brownian Motion ("BM") model that could be applied to conducting Monte Carlo Simulations, this indicator plots out the Drift factor contributing to BM. Interpretation : If the Drift value is positive, then prices are possibly moving in an uptrend. Vice versa for negative drifts.

Function - simple* Markov Chain Monte Carlo Simulation (MCMC)Example function of a markov chain monte carlo simulation.

Monte Carlo Simulation - Random Walk Hello All, Monte Carlo Simulation is a model used to predict the probability of different outcomes when the intervention of random variables is present. it is used by professionals in such widely disparate fields as finance, project management etc. You can find many articles about Monte Carlo Simulation on the net. In this script I tried to make Monte Carlo Simulation and "Random Walk". it calculates results over and over, each time using a different set of random values that is created using historical data (500 times by default) and show min-max and some random paths. number of "random walks" is calculated by using number of bars to predict, so if you change "Number of Bars to Predict" then number of random walks may change. Total number of the lines must be less than 500. "Number of Simulations " is 500 by default, more simulation better results. but if you increase it a lot then you may get "loop takes too long error" "Number of Bars to Predict" can be between 10-100 "Number of Bars to use as Data Source" is the number of historical bars to use in simulations Thanks to Ricardo Santos (@RicardoSantos) for letting me use his Random Number Generator Function. P.S. I am not mathematician and I tried to make it as far as I understood the method. so if you see any issue let me know please. Some examples: Number of Bars to Predict = 100: Number of Bars to Predict = 10: if you enable "Keep Past Min-Max Levels" option then min-max levels will stay on the chart Enjoy!

Example: Monte Carlo Simulation Experimental: Example execution of Monte Carlo Simulation applied to the markets(this is my interpretation of the algo so inconsistencys may appear). note: the algorithm is very demanding so performance is limited.