Macro Monte Carlo 10000 Prob with Bootstrap

Macro Monte Carlo 10000 Prob with Bootstrap — by Wongsakon Khaisaeng

1) Core Concept: Monte Carlo as a Macro-Probabilistic Lens on Future Price Paths

The Macro Monte Carlo 10000 Prob with Bootstrap indicator is designed to view future price evolution through a probabilistic and statistically grounded lens. Instead of predicting a single deterministic outcome, it generates thousands of simulated future price paths (Monte Carlo Paths) to estimate the range of possible outcomes. By analyzing the lowest and highest values reached within each simulated path, the indicator provides a macro-level understanding of how far price could realistically decline or rally within a specified forecast horizon. This approach shifts the focus from price forecasting to probability distribution estimation, enabling more robust decision-making for systematic traders, risk managers, and options strategists.

2) Historical Data Foundation: Extracting Log Returns as the Statistical Engine

Before any simulation takes place, the indicator constructs a historical library of logarithmic returns (log returns) derived from the asset’s recent price history. The user defines the lookback window (e.g., 1000 bars), allowing the system to characterize how returns behaved across various market regimes. Log returns are used because they preserve mathematical properties essential for multiplicative price processes, making them highly suitable for probabilistic modeling. This historical dataset forms the core statistical engine from which blocks of returns will later be sampled and recombined to create forward-looking scenarios.

3) Simulation Methodology: Block Bootstrap to Preserve Market Structure

Unlike traditional Monte Carlo methods that randomize every return independently, this indicator employs Block Bootstrap—a technique that samples consecutive clusters of returns rather than isolated points. By using these blocks (e.g., 24 bars per block), the simulation preserves vital market characteristics such as volatility clustering, trending behavior, and short-term autocorrelation. Each simulated path is built by sequentially appending multiple randomly selected return blocks until the forecast horizon is reached. This method produces realistic price trajectories that reflect the inherent temporal structure of financial markets rather than artificially smoothed or over-randomized paths.

4) Macro Perspective: Tracking Path-Level Minimums and Maximums

For each simulated price path, the indicator tracks two critical values:
(1) the lowest price reached within the entire future path, and
(2) the highest price reached within the same horizon.

This macro approach focuses on the extremes—how deep a drawdown could extend, or how high a rally could potentially reach—rather than the shape of the trajectory itself. The method reflects practical concerns in risk management and trading:

How low could price fall before my stop is hit?

How high could price rise before a take-profit trigger?

By generating thousands of such paths, the indicator builds a statistical distribution of future minimums and maximums across all simulations.

5) Percentile Bands: Converting Thousands of Paths into Statistical Insight

Once all minimum and maximum values are collected, the indicator calculates key percentiles of these distributions (e.g., 10th, 50th, 90th). These percentiles represent probabilistic thresholds:

The 10th percentile of minimums suggests a price level below which only 10% of simulated future paths ever fell.

The 90th percentile of maximums indicates a level reached by only the strongest 10% of simulated rallies.

User-defined percentile settings are then applied to generate Band Low and Band High, which are plotted on the chart at the final bar. These levels form a probabilistic corridor showing where future price movements are statistically likely—or unlikely—to reach within the chosen horizon. This creates a forward-looking “probability envelope” that adapts to volatility, market structure, and historical dynamics.

6) Touch Probabilities: Estimating the Likelihood of Hitting Key Price Levels

A defining feature of the indicator is the calculation of Touch Probabilities—the probability that price will hit a certain lower or upper level at least once within the simulation window.

The lower touch level defaults to 90% of the current spot price (unless overridden).

The upper touch level defaults to 110% of spot.

The indicator then measures the percentage of paths in which:

the path’s minimum falls below or equal to the lower level → P(Touch ≤ X)

the path’s maximum rises above or equal to the upper level → P(Touch ≥ Y)

This mirrors advanced risk-management methods in trading, especially in options pricing, where the central question is often: Will price breach a barrier within a given timeframe?
These probabilities can guide decisions related to hedging, position sizing, stop-loss design, or probability-based expectations for take-profit scenarios.

7) Visual Output: Probability Bands and a Structured Summary Table

To help traders interpret results visually, the indicator plots Band Low and Band High as horizontal forward-looking reference levels at the most recent bar. This provides a quick visual sense of the statistical “territory” price is expected to explore under randomized future paths.

Additionally, a structured summary table is displayed on-chart, presenting:

symbol

number of paths, horizon, block length

spot price

percentile metrics for min/max distributions

Band Low / Band High

touch probabilities

sample counts and lookback window

This table transforms the complex underlying simulation into a clear, interpretable snapshot ideal for systematic analysis and trading decisions.

8) Practical Interpretation: A Probability-Driven Tool for Systematic Decision-Making

The purpose of this indicator is not to generate trading signals but to provide a statistical foundation for evaluating risk and opportunity. Systematic traders can use the information to answer practical questions such as:

“Is the expected downside risk greater than the upside opportunity?”

“What is the probability that price reaches my take-profit before my stop?”

“How wide should my volatility-adjusted stop-loss realistically be?”

“Does the market currently favor expansion or contraction in price range?”

The tool can also assist in options strategies (e.g., barrier options, credit spreads), portfolio risk assessment, or position sizing in trend-following and mean-reversion systems. In short, it provides a macro-probability framework that enhances decision quality by grounding expectations in simulated statistical reality rather than subjective bias.