Self-Organized Criticality - Avalanche DistributionHere's all you need to know: This indicator applies Self-Organized Criticality (SOC) theory to financial markets, measuring the power-law exponent (alpha) of price drawdown distributions. It identifies whether markets are in stable Gaussian regimes or critical states where large cascading moves become more probable.
Self-Organized Criticality
SOC theory, introduced by Per Bak, Tang, and Wiesenfeld (1987), describes how complex systems naturally evolve toward critical (fragile) states. An example is a sand pile: adding grains creates avalanches whose sizes follow a power-law distribution rather than a normal distribution.
Financial markets exhibit similar behavior. Price movements aren't purely random walks—they display:
Fat-tailed distributions (more extreme events than Gaussian models predict)
Scale invariance (no characteristic avalanche size)
Intermittent dynamics (periods of calm punctuated by large cascades)
Power-Law Distributions
When a system is in a critical state, the probability of an avalanche of size s follows:
P(s) ∝ s^(-α)
Where:
α (alpha) is the power-law exponent
Higher α → distribution resembles Gaussian (large events rare)
Lower α → heavy tails dominate (large events common)
This indicator estimates α from the empirical distribution of price drawdowns.
Mathematical Method
1. Avalanche Detection
The indicator identifies local price peaks (highest point in a lookback window), then measures the percentage drawdown to the next trough. A dynamic ATR-based threshold filters out noise—small drops in calm markets count, but the bar rises in volatile periods.
2. Logarithmic Binning
Avalanche sizes are sorted into logarithmically-spaced bins (e.g., 1-2%, 2-4%, 4-8%) rather than linear bins. This captures power-law behavior across multiple scales - a 2% drop and 20% crash both matter. The indicator creates 12 adaptive bins spanning from your smallest to largest observed avalanche.
3. Bin-to-Bin Ratio Estimation
For each pair of adjacent bins, we calculate:
α ≈ log(N₁/N₂) / log(s₂/s₁)
Where N₁ and N₂ are avalanche counts, s₁ and s₂ are bin sizes.
Example: If 2% drops happen 4× more often than 4% drops, then α ≈ log(4)/log(2) ≈ 2.0.
We get 8-11 independent estimates and average them. This is more robust than fitting one line through all points—outliers can't dominate.
4. Rolling Window Analysis
Alpha recalculates using only recent avalanches (default: last 500 bars). Old data drops out as new avalanches occur, so the indicator tracks regime shifts in real-time.
Regime Classification
🟢 Gaussian α ≥ 2.8 Normal distribution behavior; large moves are rare outliers
🟡 Transitional 1.8 ≤ α < 2.8 Moderate fat tails; system approaching criticality
🟠 Critical 1.0 ≤ α < 1.8 Heavy tails; large avalanches increasingly common
🔴 Super-Critical α < 1.0 Extreme tail risk; system prone to cascading failures
What Alpha Tells You
Declining alpha → Market moving toward criticality; tail risk increasing
Rising alpha → Market stabilizing; returns to normal distribution
Persistent low alpha → Sustained fragility; heightened crash probability
Supporting Metrics
Heavy Tail %: Concentration of total drawdown in largest 10% of events
Populated Bins: Data coverage quality (11-12 out of 12 is ideal)
Avalanche Count: Sample size for statistical reliability
Limitations
This is a distributional measure, not a timing indicator. Low alpha indicates increased systemic risk but doesn't predict when a cascade will occur. Only that the probability distribution has shifted toward larger events.
How This Differs from the Per Bak Fragility Index
The SOC Avalanche Distribution calculates the power-law exponent (alpha) directly from price drawdown distributions - a pure mathematical analysis requiring only price data. The Per Bak Fragility Index aggregates external stress indicators (VIX, SKEW, credit spreads, put/call ratios) into a weighted composite score.
Technical Notes
Default settings optimized for daily and weekly timeframes on major indices
Requires minimum 200 bars of history for stable estimates
ATR-based dynamic sizing prevents scale-dependent bias
Alerts available for regime transitions and super-critical entry
References
Bak, P., Tang, C., & Wiesenfeld, K. (1987). Self-organized criticality: An explanation of the 1/f noise. Physical Review Letters.
Sornette, D. (2003). Why Stock Markets Crash: Critical Events in Complex Financial Systems. Princeton University Press.
Perbak
Per Bak Self-Organized CriticalityTL;DR: This indicator measures market fragility. It measures the system's vulnerability to cascade failures and phase transitions. I've added four independent stress vectors: tail risk, volatility regime, credit stress, and positioning extremes. This allows us to quantify how susceptible markets are to disproportionate moves from small shocks, similar to how a steep sandpile is primed for avalanches.
Avalanches, forest fires, earthquakes, pandemic outbreaks, and market crashes. What do they all have in common? They are not random.
These events follow power laws - stable systems that naturally evolve toward critical states where small triggers can unleash catastrophic cascades.
For example, if you are building a sandpile, there will be a point with a little bit additional sand will cause a landslide.
Markets build fragility grain by grain, like a sandpile approaching avalanche.
The Per Bak Self-Organized Criticality (SOC) indicator detects when the markets are a few grains away from collapse.
This indicator is highly inspired by the work of Per Bak related to the science of self-organized criticality .
As Bak said:
"The earthquake does not 'know how large it will become'. Thus, any precursor state of a large event is essentially identical to a precursor state of a small event."
For markets, this means:
We cannot predict individual crash size from initial conditions
We can predict statistical distribution of crashes
We can identify periods of increased systemic risk (proximity to critical state)
BTW, this is a forwarding looking indicator and doesn't reprint. :)
The Story of Per Bak
In 1987, Danish physicist Per Bak and his colleagues discovered an important pattern in nature: self-organized criticality.
Their sandpile experiment revealed something: drop grains of sand one by one onto a pile, and the system naturally evolves toward a critical state. Most grains cause nothing. Some trigger small slides. But occasionally a single grain triggers a massive avalanche.
The key insight is that we cannot predict which grain will trigger the avalanche, but you can measure when the pile has reached a critical state.
Why Markets Are the Ultimate SOC System?
Financial markets exhibit all the hallmarks of self-organized criticality:
Interconnected agents (traders, institutions, algorithms) with feedback loops
Non-linear interactions where small events can cascade through the system
Power-law distributions of returns (fat tails, not normal distributions)
Natural evolution toward fragility as leverage builds, correlations tighten, and positioning crowds
Phase transitions where calm markets suddenly shift to crisis regimes
Mathematical Foundation
Power Law Distributions
Traditional finance assumes returns follow a normal distribution. "Markets return 10% on average." But I disagree. Markets follow power laws:
P(x) ∝ x^(-α)
Where P(x) is the probability of an event of size x, and α is the power law exponent (typically 3-4 for financial markets).
What this means: Small moves happen constantly. Medium moves are less frequent. Catastrophic moves are rare but follow predictable probability distributions. The "fat tails" are features of critical systems.
Critical Slowing Down
As systems approach phase transitions, they exhibit critical slowing down—reduced ability to absorb shocks. Mathematically, this appears as:
τ ∝ |T - T_c|^(-ν)
Where τ is the relaxation time, T is the current state, T_c is the critical threshold, and ν is the critical exponent.
Translation: Near criticality, markets take longer to recover from perturbations. Fragility compounds.
Component Aggregation & Non-Linear Emergence
The Per Bak SOC our index aggregates four normalized components (each scaled 0-100) with tunable weights:
SOC = w₁·C_tail + w₂·C_vol + w₃·C_credit + w₄·C_position
Default weights (you can change this):
w₁ = 0.34 (Tail Risk via SKEW)
w₂ = 0.26 (Volatility Regime via VIX term structure)
w₃ = 0.18 (Credit Stress via HYG/LQD + TED spread)
w₄ = 0.22 (Positioning Extremes via Put/Call ratio)
Each component uses percentile ranking over a 252-day lookback combined with absolute thresholds to capture both relative regime shifts and extreme absolute levels.
The Four Pillars Explained
1. Tail Risk (SKEW Index)
Measures options market pricing of fat-tail events. High SKEW indicates elevated outlier probability.
C_tail = 0.7·percentrank(SKEW, 252) + 0.3·((SKEW - 115)/0.5)
2. Volatility Regime (VIX Term Structure)
Combines VIX level with term structure slope. Backwardation signals acute stress.
C_vol = 0.4·VIX_level + 0.35·VIX_slope + 0.25·VIX_ratio
3. Credit Stress (HYG/LQD + TED Spread)
Tracks high-yield deterioration versus investment-grade and interbank lending stress.
C_credit = 0.65·percentrank(LQD/HYG, 252) + 0.35·(TED/0.75)·100
4. Positioning Extremes (Put/Call Ratio)
Detects extreme hedging demand through percentile ranking and z-score analysis.
C_position = 0.6·percentrank(P/C, 252) + 0.4·zscore_normalized
What the Indicator Really Measures?
Not Volatility but Fragility
Markets Going Down ≠ Fragility Building (actually when markets go down, risk and fragility are released)
The 0-100 Scale & Regime Thresholds
The indicator outputs a 0-100 fragility score with four regimes:
🟢 Safe (0-39): System resilient, can absorb normal shocks
🟡 Building (40-54): Early fragility signs, watch for deterioration
🟠 Elevated (55-69): System vulnerable
🔴 Critical (70-100): Highly susceptible to cascade failures
Further Reading for Nerds
Bak, P., Tang, C., & Wiesenfeld, K. (1987). "Self-organized criticality: An explanation of 1/f noise." Physical Review Letters.
Bak, P. & Chen, K. (1991). "Self-organized criticality." Scientific American.
Bak, P. (1996). How Nature Works: The Science of Self-Organized Criticality. Copernicus.
Feedback is appreciated :)
