Per Bak Self-Organized Criticality

TL;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 :)