First Passage Time - Distribution AnalysisThe First Passage Time (FPT) Distribution Analysis indicator is a sophisticated probabilistic tool that answers one of the most critical questions in trading: "How long will it take for price to reach my target, and what are the odds of getting there first?"
Unlike traditional technical indicators that focus on what might happen, this indicator tells you when it's likely to happen.
Mathematical Foundation: First Passage Time Theory
What is First Passage Time?
First Passage Time (FPT) is a concept in stochastic processes that measures the time it takes for a random process to reach a specific threshold for the first time. Originally developed in physics and mathematics, FPT has applications in:
Quantitative Finance: Option pricing, risk management, and algorithmic trading
Neuroscience: Modeling neural firing patterns
Biology: Population dynamics and disease spread
Engineering: Reliability analysis and failure prediction
The Mathematics Behind It
This indicator uses Geometric Brownian Motion (GBM), the same stochastic model used in the Black-Scholes option pricing formula:
dS = μS dt + σS dW
Where:
S = Asset price
μ = Drift (trend component)
σ = Volatility (uncertainty component)
dW = Wiener process (random walk)
Through Monte Carlo simulation, the indicator runs 1,000+ price path simulations to statistically determine:
When each threshold (+X% or -X%) is likely to be hit
Which threshold is hit first (directional bias)
How often each scenario occurs (probability distribution)
🎯 How This Indicator Works
Core Algorithm Workflow:
Calculate Historical Statistics
Measures recent price volatility (standard deviation of log returns)
Calculates drift (average directional movement)
Annualizes these metrics for meaningful comparison
Run Monte Carlo Simulations
Generates 1,000+ random price paths based on historical behavior
Tracks when each path hits the upside (+X%) or downside (-X%) threshold
Records which threshold was hit first in each simulation
Aggregate Statistical Results
Calculates percentile distributions (10th, 25th, 50th, 75th, 90th)
Computes "first hit" probabilities (upside vs downside)
Determines average and median time-to-target
Visual Representation
Displays thresholds as horizontal lines
Shows gradient risk zones (purple-to-blue)
Provides comprehensive statistics table
📈 Use Cases
1. Options Trading
Selling Options: Determine if your strike price is likely to be hit before expiration
Buying Options: Estimate probability of reaching profit targets within your time window
Time Decay Management: Compare expected time-to-target vs theta decay
Example: You're considering selling a 30-day call option 5% out of the money. The indicator shows there's a 72% chance price hits +5% within 12 days. This tells you the trade has high assignment risk.
2. Swing Trading
Entry Timing: Wait for higher probability setups when directional bias is strong
Target Setting: Use median time-to-target to set realistic profit expectations
Stop Loss Placement: Understand probability of hitting your stop before target
Example: The indicator shows 85% upside probability with median time of 3.2 days. You can confidently enter long positions with appropriate position sizing.
3. Risk Management
Position Sizing: Larger positions when probability heavily favors one direction
Portfolio Allocation: Reduce exposure when probabilities are near 50/50 (high uncertainty)
Hedge Timing: Know when to add protective positions based on downside probability
Example: Indicator shows 55% upside vs 45% downside—nearly neutral. This signals high uncertainty, suggesting reduced position size or wait for better setup.
4. Market Regime Detection
Trending Markets: High directional bias (70%+ one direction)
Range-bound Markets: Balanced probabilities (45-55% both directions)
Volatility Regimes: Compare actual vs theoretical minimum time
Example: Consistent 90%+ bullish bias across multiple timeframes confirms strong uptrend—stay long and avoid counter-trend trades.
First Hit Rate (Most Important!)
Shows which threshold is likely to be hit FIRST:
Upside %: Probability of hitting upside target before downside
Downside %: Probability of hitting downside target before upside
These always sum to 100%
⚠️ Warning: If you see "Low Hit Rate" warning, increase this parameter!
Advanced Parameters
Drift Mode
Allows you to explore different scenarios:
Historical: Uses actual recent trend (default—most realistic)
Zero (Neutral): Assumes no trend, only volatility (symmetric probabilities)
50% Reduced: Dampens trend effect (conservative scenario)
Use Case: Switch to "Zero (Neutral)" to see what happens in a pure volatility environment, useful for range-bound markets.
Distribution Type
Percentile: Shows 10%, 25%, 50%, 75%, 90% levels (recommended for most users)
Sigma: Shows standard deviation levels (1σ, 2σ)—useful for statistical analysis
⚠️ Important Limitations & Best Practices
Limitations
Assumes GBM: Real markets have fat tails, jumps, and regime changes not captured by GBM
Historical Parameters: Uses recent volatility/drift—may not predict regime shifts
No Fundamental Events: Cannot predict earnings, news, or macro shocks
Computational: Runs only on last bar—doesn't give historical signals
Remember: Probabilities are not certainties. Use this indicator as part of a comprehensive trading plan with proper risk management.
Created by: Henrique Centieiro. feedback is more than welcome!
