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Markov + Monte Carlo Simulation with EV
Markov Monte Carlo Projection (MMCP) – A Probabilistic Approach to Price Forecasting
Introduction: A New Approach to Price Projection
The Markov Monte Carlo Projection (MMCP) is an advanced stochastic forecasting tool that models potential future price paths using a combination of Markov Chain transition probabilities and Monte Carlo simulations. Unlike traditional technical indicators that rely on fixed formulas, MMCP employs probability distributions and simulated price movement paths to estimate future price behavior dynamically.
This indicator is designed to adapt to changing market conditions and provides traders with a probabilistic framework rather than a fixed forecast. By incorporating volatility modeling, MMCP enables traders to size projections proportionally to recent price action, making it an adaptive and flexible forecasting tool.
Mathematical Foundations
Markov Chains: Modeling Probability of Price Movements
A Markov Chain is a stochastic process where the probability of transitioning to the next state depends only on the current state and not on past states (i.e., it is memoryless).
For price movement, MMCP analyzes the past N bars (set by the lookback window) to determine the transition probabilities of price moving up, down, or remaining the same based on past behavior:
Pup=Number of Up MovesTotal Moves
Pup=Total MovesNumber of Up Moves
Pdown=Number of Down MovesTotal Moves
Pdown=Total MovesNumber of Down Moves
Psame=1−(Pup+Pdown)
Psame=1−(Pup+Pdown)
These probabilities guide how future price movements are simulated, ensuring that projections reflect historical price behavior tendencies.
Monte Carlo Simulations: Generating Possible Futures
Monte Carlo simulations involve running many random trials to estimate possible outcomes. Each trial simulates a future price path by:
Randomly selecting a direction based on the Markov probabilities Pup,Pdown,PsamePup,Pdown,Psame.
Determining the magnitude of the price movement using a normally distributed volatility model.
Iterating this process across multiple forecast bars to simulate a range of potential price paths.
This process does not predict a single outcome, but rather generates a probability-weighted range of future price possibilities.
Volatility Modeling: Scaling Movements Proportionally
Why We Use Standard Deviation (σσ)
Price movement is inherently volatile, and the magnitude of price shifts must be scaled relative to recent volatility. MMCP calculates rolling price returns and then derives the standard deviation of those returns:
σ=stdev(price returns,lookback)
σ=stdev(price returns,lookback)
The Volatility Multiplier allows users to adjust the impact of this volatility on projected movements. This makes the indicator adaptive to different asset price ranges.
Key User Adjustments
1. Volatility Multiplier – Tuning Projections for Different Assets
The scale of the Volatility Multiplier must be tuned for each asset because it is relative to the magnitude of price action. For example:
Low-priced assets (e.g., $2.50 stocks) → A multiplier of 0.1 works best.
Mid-priced assets (e.g., $250 stocks) → A multiplier of 3 works best.
High-priced assets (e.g., Bitcoin) → A multiplier of 1000 works best.
🔹 If projections seem too extreme, decrease the multiplier.
🔹 If projections seem too flat, increase the multiplier.
The Volatility Multiplier can also be fine-tuned to make the projected signal proportionate to the immediately preceding price action.
2. Expected Value (EV) Path – Analyzing Aggregate Future Probabilities
The EV Line is a computed average of all simulated paths, giving traders an expected mean trajectory.
If you find that the EV Line is not visible, try increasing the volatility multiplier to make it more pronounced.
3. Projection Inversion – Enhancing Analysis with Paired Indicators
A unique feature of MMCP is the projection inversion toggle, designed to allow traders to run multiple instances of the indicator in tandem.
When one instance is set to normal projection and another to inverted projection, traders can pair them together using identical settings (except inversion). This setup allows for a mirrored probability perspective and enhances visualizing volatility dynamics.
Additionally, traders can use multiple sets of paired indicators, each with a different lookback window, to build a multi-layered, probability-driven market visualization. This dynamic approach provides an evolving structure of probable price movement in different time frames, offering deeper insights into potential market conditions.
How MMCP Works in Real-Time
Each new bar triggers a fresh Monte Carlo simulation, meaning that projections organically evolve with the market. This ensures that MMCP is always responding to current conditions, rather than applying static assumptions.
How to Use MMCP in Trading
✔ Identifying Potential Reversal & Continuation Zones
If most Monte Carlo paths project upward, bullish momentum is likely.
If most Monte Carlo paths project downward, bearish momentum is likely.
The Expected Value (EV) Line can help confirm the most probable trajectory.
✔ Analyzing Market Sentiment in Real Time
Use multiple instances of MMCP with different lookback windows to capture short-term vs. long-term sentiment.
Enable projection inversion to analyze potential mirrored moves.
✔ Fine-Tuning MMCP for Your Strategy
Adjust the Volatility Multiplier to match the price scale of your asset.
Increase the number of simulations to improve statistical robustness.
Use shorter lookback windows for more responsive predictions, or longer windows for more stable forecasts.
Why MMCP is a Game-Changer
✅ Dynamic & Probabilistic – Unlike fixed indicators, MMCP adapts in real-time.
✅ Fully Stochastic – MMCP embraces uncertainty using Markov models & Monte Carlo simulations.
✅ Customizable for Any Asset – Adjust the Volatility Multiplier for small or large price movements.
✅ Live Updates – The projection organically evolves with every new price bar.
✅ Multi-Perspective Analysis – Traders can run paired normal and inverted projections for deeper insights.
By tuning Volatility Multiplier, Lookback Window, and Projection Inversion, traders can customize MMCP to fit their strategy.
Final Thoughts
The Markov Monte Carlo Projection (MMCP) is not about making absolute predictions—it is about understanding probability distributions in price action.
By leveraging Monte Carlo simulations, Markov transition probabilities, and dynamic volatility modeling, MMCP gives traders a powerful probability-based edge in forecasting potential price movement.
Introduction: A New Approach to Price Projection
The Markov Monte Carlo Projection (MMCP) is an advanced stochastic forecasting tool that models potential future price paths using a combination of Markov Chain transition probabilities and Monte Carlo simulations. Unlike traditional technical indicators that rely on fixed formulas, MMCP employs probability distributions and simulated price movement paths to estimate future price behavior dynamically.
This indicator is designed to adapt to changing market conditions and provides traders with a probabilistic framework rather than a fixed forecast. By incorporating volatility modeling, MMCP enables traders to size projections proportionally to recent price action, making it an adaptive and flexible forecasting tool.
Mathematical Foundations
Markov Chains: Modeling Probability of Price Movements
A Markov Chain is a stochastic process where the probability of transitioning to the next state depends only on the current state and not on past states (i.e., it is memoryless).
For price movement, MMCP analyzes the past N bars (set by the lookback window) to determine the transition probabilities of price moving up, down, or remaining the same based on past behavior:
Pup=Number of Up MovesTotal Moves
Pup=Total MovesNumber of Up Moves
Pdown=Number of Down MovesTotal Moves
Pdown=Total MovesNumber of Down Moves
Psame=1−(Pup+Pdown)
Psame=1−(Pup+Pdown)
These probabilities guide how future price movements are simulated, ensuring that projections reflect historical price behavior tendencies.
Monte Carlo Simulations: Generating Possible Futures
Monte Carlo simulations involve running many random trials to estimate possible outcomes. Each trial simulates a future price path by:
Randomly selecting a direction based on the Markov probabilities Pup,Pdown,PsamePup,Pdown,Psame.
Determining the magnitude of the price movement using a normally distributed volatility model.
Iterating this process across multiple forecast bars to simulate a range of potential price paths.
This process does not predict a single outcome, but rather generates a probability-weighted range of future price possibilities.
Volatility Modeling: Scaling Movements Proportionally
Why We Use Standard Deviation (σσ)
Price movement is inherently volatile, and the magnitude of price shifts must be scaled relative to recent volatility. MMCP calculates rolling price returns and then derives the standard deviation of those returns:
σ=stdev(price returns,lookback)
σ=stdev(price returns,lookback)
The Volatility Multiplier allows users to adjust the impact of this volatility on projected movements. This makes the indicator adaptive to different asset price ranges.
Key User Adjustments
1. Volatility Multiplier – Tuning Projections for Different Assets
The scale of the Volatility Multiplier must be tuned for each asset because it is relative to the magnitude of price action. For example:
Low-priced assets (e.g., $2.50 stocks) → A multiplier of 0.1 works best.
Mid-priced assets (e.g., $250 stocks) → A multiplier of 3 works best.
High-priced assets (e.g., Bitcoin) → A multiplier of 1000 works best.
🔹 If projections seem too extreme, decrease the multiplier.
🔹 If projections seem too flat, increase the multiplier.
The Volatility Multiplier can also be fine-tuned to make the projected signal proportionate to the immediately preceding price action.
2. Expected Value (EV) Path – Analyzing Aggregate Future Probabilities
The EV Line is a computed average of all simulated paths, giving traders an expected mean trajectory.
If you find that the EV Line is not visible, try increasing the volatility multiplier to make it more pronounced.
3. Projection Inversion – Enhancing Analysis with Paired Indicators
A unique feature of MMCP is the projection inversion toggle, designed to allow traders to run multiple instances of the indicator in tandem.
When one instance is set to normal projection and another to inverted projection, traders can pair them together using identical settings (except inversion). This setup allows for a mirrored probability perspective and enhances visualizing volatility dynamics.
Additionally, traders can use multiple sets of paired indicators, each with a different lookback window, to build a multi-layered, probability-driven market visualization. This dynamic approach provides an evolving structure of probable price movement in different time frames, offering deeper insights into potential market conditions.
How MMCP Works in Real-Time
Each new bar triggers a fresh Monte Carlo simulation, meaning that projections organically evolve with the market. This ensures that MMCP is always responding to current conditions, rather than applying static assumptions.
How to Use MMCP in Trading
✔ Identifying Potential Reversal & Continuation Zones
If most Monte Carlo paths project upward, bullish momentum is likely.
If most Monte Carlo paths project downward, bearish momentum is likely.
The Expected Value (EV) Line can help confirm the most probable trajectory.
✔ Analyzing Market Sentiment in Real Time
Use multiple instances of MMCP with different lookback windows to capture short-term vs. long-term sentiment.
Enable projection inversion to analyze potential mirrored moves.
✔ Fine-Tuning MMCP for Your Strategy
Adjust the Volatility Multiplier to match the price scale of your asset.
Increase the number of simulations to improve statistical robustness.
Use shorter lookback windows for more responsive predictions, or longer windows for more stable forecasts.
Why MMCP is a Game-Changer
✅ Dynamic & Probabilistic – Unlike fixed indicators, MMCP adapts in real-time.
✅ Fully Stochastic – MMCP embraces uncertainty using Markov models & Monte Carlo simulations.
✅ Customizable for Any Asset – Adjust the Volatility Multiplier for small or large price movements.
✅ Live Updates – The projection organically evolves with every new price bar.
✅ Multi-Perspective Analysis – Traders can run paired normal and inverted projections for deeper insights.
By tuning Volatility Multiplier, Lookback Window, and Projection Inversion, traders can customize MMCP to fit their strategy.
Final Thoughts
The Markov Monte Carlo Projection (MMCP) is not about making absolute predictions—it is about understanding probability distributions in price action.
By leveraging Monte Carlo simulations, Markov transition probabilities, and dynamic volatility modeling, MMCP gives traders a powerful probability-based edge in forecasting potential price movement.
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