M Carlo Pro -> PROFABIGHI_CAPITAL

🌟 Overview

The M Carlo Pro is a sophisticated Monte Carlo simulation engine that generates probabilistic price projections and scenario analysis frameworks. It offers dual-mode operation combining forward-looking price path modeling with return-based scenario testing, featuring confidence interval calculations, histogram distribution analysis, and customizable random sampling from historical data or user-defined return distributions.

⚙️ Main Mode Selector

- Analysis Mode Choice: Select between Scenario Analysis or Price Projection
- Scenario Analysis: Return-based simulations displayed in separate indicator pane with distribution analysis
- Price Projection: Forward price paths rendered directly on main price chart
- Mode-Specific Visualization: Each mode optimizes display for its analytical purpose

📊 Common Simulation Settings

- Random Seed: Fixed seed value for reproducible simulation results across multiple runs
- Distribution Type Selection: Choose between Normal (Gaussian) distribution or Bootstrap resampling
- Number of Paths: Total simulation iterations to generate for statistical validity
- Projection Length: Forward-looking bars or steps for each simulation path
- Boundaries Only Toggle: Display only confidence bounds instead of full path ensemble
- Historical Lookback: Number of past bars to collect for return distribution calculation
- Path Style Selector: Visual line style (solid, dotted, or dashed) for rendered paths

📈 Scenario Analysis Settings

Simulation Source Options:
- Price Mode: Calculates returns from historical price data automatically
- Custom Returns Mode: Uses user-defined return values for scenario testing

Return Input Framework:
- Primary Returns: Main scenario return values entered as text (one per line)
- Secondary Returns: Additional scenario layer for multi-dimensional analysis
- Tertiary Returns: Third scenario dimension for complex modeling
- Quaternary Returns: Fourth scenario layer for maximum flexibility
- Multi-Layer Support: Combine multiple return sets for comprehensive scenario coverage

Confidence and Display:
- Confidence Level Percentage: Statistical confidence interval for boundary calculations
- Path Lines Only: Show simulation paths without additional visual elements
- Scatter Plot Mode: Render final outcomes as scatter points instead of connected paths
- Distribution View Only: Display exclusively the histogram distribution without paths

Histogram Configuration:
- Binning Method Selection: Choose between Sturges, Rice, Square Root, or custom bin calculation
- Automatic Bin Sizing: Statistical formulas determine optimal histogram granularity
- Custom Bin Option: Manual specification of histogram bar count when custom method selected

📈 Price Projection Settings

- Display Scale Toggle: Show or hide price axis and scale labels on projection chart
- Force Render Option: Override path limit for full rendering (may truncate long projections)
- Show Mean Path: Display the average projection path across all simulations for central tendency visualization
- Performance Table: Summary statistics showing number of paths generated and projection length

🔧 Distribution Methods

Normal Distribution (Gaussian):
- Calculates mean and standard deviation from historical returns
- Generates random values using Box-Muller transform
- Produces symmetric probability distribution around mean
- Two independent uniform random numbers transformed into normally distributed values

Bootstrap Resampling:
- Randomly samples from actual historical return observations
- Preserves empirical distribution characteristics without parametric assumptions
- Each simulation step selects one historical return with replacement
- Captures real market behavior including fat tails and skewness

Return Calculation Logic:
- Price Mode: Logarithmic returns calculated from consecutive price ratios
- Custom Mode: User-provided returns applied directly to simulation
- Exponential Application: Price mode uses exponential of return for price updates
- Additive Application: Custom return mode adds returns directly

📊 Scenario Analysis Execution

Simulation Loop Process:
- Initialize starting value (price or sum of returns)
- Generate random return using selected distribution method
- Apply return to current value using appropriate calculation method
- Store intermediate results in matrix structure
- Track final outcomes in endpoint array
- Repeat for specified number of paths

Confidence Interval Calculation:
- Bins final outcomes into histogram with chosen binning method
- Identifies bin with maximum frequency (mode)
- Expands range symmetrically around mode
- Calculates cumulative probability of range
- Highlights bins within specified confidence level
- Displays confidence percentage and visual fill

Visualization Components:
- Path Rendering: Colored lines showing individual simulation trajectories
- Scatter Plot Option: Final outcomes plotted as individual points with labels or boxes
- Boundary Lines: Orange and teal lines marking confidence envelope when boundaries-only enabled
- Current Sum Line: Yellow reference line showing starting return sum in custom mode
- Step Labels: Bar numbers or step counts along horizontal axis
- Scale Axes: Vertical scale with value labels and horizontal baseline

📈 Price Projection Execution

Path Generation Framework:
- Divides total paths into twenty batches for performance optimization
- Each batch processes assigned number of simulations
- Generates forward price points using distribution sampling
- Accumulates sum of all prices at each projection step for average calculation
- Stores endpoints for statistical analysis
- Renders paths as polylines with random color assignment

Mean Path Calculation:
- Sums all simulated prices at each forward bar
- Divides by total number of simulations for average
- Plots thicker aqua-colored line representing expected value path
- Provides central tendency reference across all scenarios

Performance Optimization:
- Batch Processing: Splits simulations into manageable chunks
- Point Aggregation: Collects points before polyline rendering
- Conditional Rendering: Force option overrides automatic path limits
- Dynamic Coloring: Random RGB generation for path differentiation

Scale and Annotation:
- Vertical Scale: Price axis with evenly spaced labels showing projection range
- Horizontal Scale: Bar count labels showing forward projection timeline
- Grid Lines: Teal-colored axes forming scale framework
- Performance Table: Bottom-right display of simulation parameters

🎨 Visualization Features

Scenario Analysis Display (Separate Pane):
- Simulation Paths: Multi-colored trajectories from starting point to projection horizon
- Baseline Plot: Aqua line showing starting value (price or return sum)
- Confidence Boundaries: Orange (lower) and teal (upper) envelope lines
- Histogram Distribution: Orange bars showing frequency of final outcomes
- Bin Labels: Outcome values and frequencies displayed on each histogram bar
- Confidence Highlight: Darker orange shading on bins within confidence interval
- Confidence Label: Percentage display showing statistical coverage
- Axis Scaling: Adaptive vertical scale based on outcome range

Price Projection Display (Main Chart):
- Price Candles: Teal (bullish) or orange (bearish) candles on underlying price chart
- Projection Paths: Rainbow-colored polylines extending forward from current bar
- Mean Path Line: Thick aqua line showing average projection across all simulations
- Scale Display: Optional price axis and bar count labels
- Performance Table: Summary box showing simulation statistics

Common Visual Elements:
- Random Coloring: Each path assigned unique RGB values for differentiation
- Line Style Options: Solid, dotted, or dashed rendering for all paths
- Transparent Colors: Semi-transparent fills and lines prevent visual clutter
- Dynamic Scaling: Automatic axis adjustment based on outcome distribution

🔍 Advanced Features

Matrix Data Management:
- Row-Column Structure: Simulation results stored in two-dimensional matrix
- Color Matrix: Parallel matrix storing path colors for rendering
- Min-Max Tracking: Boundary matrix records extremes at each projection step
- Endpoint Array: Final outcome values collected for histogram analysis

Histogram Construction:
- Automatic Binning: Statistical formulas calculate optimal bin count based on sample size
- Sturges Formula: Logarithmic approach for bin determination
- Rice Rule: Cube-root-based calculation for granularity
- Square Root Method: Simple square root of sample size
- Frequency Counting: Each outcome assigned to appropriate bin
- Value Tracking: Minimum value in each bin recorded for labeling

Scatter Plot Implementation:
- Label Creation: First 500 outcomes rendered as styled labels with circular markers
- Box Fallback: Additional outcomes beyond label limit rendered as boxes
- Random Positioning: X-coordinate randomization prevents perfect vertical alignment
- Color Preservation: Each point retains its assigned simulation color

Adaptive Visualization:
- Mode Detection: Different rendering logic for price versus return simulations
- Toggle Interactions: Boundary-only and histogram-only modes override default displays
- Dynamic Limits: Path rendering adjusts based on performance constraints
- Conditional Elements: Scale, mean, and table displays controlled by user toggles

🎯 Use Cases and Applications

Risk Assessment:
- Generate probability distribution of future outcomes
- Identify worst-case and best-case scenarios with confidence intervals
- Quantify likelihood of specific price targets
- Visualize range of plausible futures based on historical volatility

Scenario Planning:
- Test specific return sequences using custom input mode
- Model multiple market environments with layered return sets
- Compare outcomes across different volatility assumptions
- Evaluate strategy performance under various conditions

Portfolio Projections:
- Forecast future portfolio values with probabilistic bounds
- Estimate expected returns across multiple timeframes
- Assess probability of reaching financial goals
- Understand distribution of potential outcomes

Education and Research:
- Demonstrate Monte Carlo methodology visually
- Explore effects of different distribution assumptions
- Compare normal versus empirical (bootstrap) distributions
- Illustrate concepts of confidence intervals and central limit theorem

✅ Key Takeaways

- Dual-Mode Flexibility: Scenario Analysis for distribution study or Price Projection for forward visualization
- Statistical Rigor: Confidence interval calculation with automatic histogram binning methods
- Distribution Choices: Normal (Gaussian) assumption or Bootstrap for empirical distribution preservation
- Custom Scenario Testing: Four-layer return input system for complex multi-dimensional analysis
- Reproducible Results: Fixed random seed ensures consistent output across multiple runs
- Batch Processing Optimization: Twenty-batch execution for handling large simulation counts
- Visual Clarity: Separate pane for scenario analysis, main chart overlay for price projections
- Mean Path Reference: Average trajectory across all simulations provides expected value guidance
- Adaptive Scaling: Automatic axis adjustment and range detection for optimal display
- Performance Management: Conditional rendering limits and force options balance detail with execution speed
- Histogram Intelligence: Multiple binning algorithms with confidence highlighting for outcome distribution
- Comprehensive Visualization: Paths, boundaries, scatter plots, histograms, scales, and tables for complete analytical picture