# Monte Carlo Price Probabilities

Monte Carlo simulations have been a popular tool in the world of finance, risk analysis, and decision making for decades. In this post, I will take you through the history of Monte Carlo simulations and explain how I implemented this powerful technique in Pine Script. This implementation can help traders and investors in various time frames to better understand the potential future price movements of financial instruments based on historical data.

History of Monte Carlo Simulations

The Monte Carlo method was named after the famous Monte Carlo Casino in Monaco, as the technique involves using random sampling to approximate solutions to mathematical problems. The method was first introduced by Stanislaw Ulam, a mathematician working on the Manhattan Project in the 1940s. Ulam realized that using random sampling could provide approximate solutions to complex problems that were otherwise difficult or impossible to solve analytically.

Over the years, Monte Carlo simulations have found applications in various fields, including physics, engineering, and finance. In the world of finance, the method has been used to model stock price movements, option pricing, portfolio optimization, and risk management.

Implementation in Pine

In my implementation of Monte Carlo simulations in Pine, I created a script that allows users to input several parameters such as the arbitrary price, number of simulations, number of steps into the future, and the start bar index. The start bar index is a crucial setting for running the script on lower time frames, as it helps to ensure that the script runs smoothly for a given symbol.

The script then calculates the log return of each bar and categorizes them into green (positive) or red (negative) moves. It uses these historical price movements to calculate the probabilities of future price movements for each step in the simulation.

The core of the Monte Carlo simulation lies in the `monte()` function, which generates random numbers to determine if the next price movement will be green or red, and then selects a move size based on its probability. The `sim()` function runs multiple simulations using the `monte()` function and stores the results in an array.

Finally, the script calculates the probability of the arbitrary price being reached in the future based on the results of the simulations. It also plots the probability on the chart, allowing users to visually assess the potential future price movements of the financial instrument.

Using the Monte Carlo Simulation

To use the Monte Carlo simulation in Pine, you need to input the desired parameters such as the arbitrary price, number of simulations, number of steps into the future, and the start bar index. For some symbols, you may need to set the start bar index to around 10k to ensure that the script runs smoothly.

Once you have input the parameters and run the script, you will see the probability of reaching the arbitrary price plotted on the chart. This can provide a valuable insight into the potential future price movements of the financial instrument based on historical data, helping you make more informed trading and investment decisions.

Conclusion

Monte Carlo simulations have a rich history and have proven to be a valuable tool in various fields, including finance. My implementation of Monte Carlo simulations in Pine allows traders and investors to better understand the potential future price movements of financial instruments in various time frames. By evaluating the probabilities of reaching specific price levels, users can make more informed decisions and better manage their risk.
Versionsinformation:
added rounding to help it run on lower time frames
Versionsinformation:
Fixed the probability repaint issue, which resulted in more accurate and consistent probability calculations.
Added a label to display the number of bars, allowing users to set the start bar index appropriately.
Modified the script to calculate the start bar index by subtracting the lookback value from the bar index (bar_index - 100). This allows for more control over the lookback period and ensures that the correct start bar index is used.
In this new version of the script, the probability repaint issue has been fixed, providing more accurate probability calculations. The addition of a label helps users identify the number of bars and set the start bar index accordingly. Additionally, the start bar index calculation has been improved by allowing users to define a lookback period, ensuring the correct start bar index is used in calculations.
Versionsinformation:
unfixed repaint
Versionsinformation:
I think I fixed repaint

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