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.


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:

1. Collect each bar's price changes in the user-set window.
   
2. Randomize the order of each change in the window.
   
3. Project the cumulative sum of the shuffled changes from the current closing price.
   
4. 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.