econophysics

name: econophysics description: Physics methods for financial markets license: MIT metadata: audience: researchers category: interdisciplinary

What I do

• Apply statistical physics to financial systems
• Model market dynamics and crashes
• Analyze price fluctuations and correlations
• Predict market behavior patterns
• Study risk and wealth distributions

When to use me

When analyzing financial data, modeling economic systems, or predicting market behavior using physics-based approaches.

Key Concepts

Statistical Properties

Power Laws: P(x) ~ x^(-α)
- Wealth distribution (Pareto)
- Stock returns (fat tails)
- City sizes (Zipf's law)

Scaling Laws:
- Volatility clustering
- Long-range correlations
- Multifractal behavior

Key Models

Black-Scholes: Option pricing via PDE
ARCH/GARCH: Volatility clustering
Hawkes Processes: Event cascades

Market Phenomena

• Fat-tailed return distributions
• Volatility clustering
• Anti-correlations in sign
• Market crashes (phase transitions)
• Herding behavior

Correlation Analysis

# Correlation matrix analysis
import numpy as np

# Eigenvalue spectrum (Marchenko-Pastur)
# Random matrix theory filtering
# Minimum spanning tree networks

Risk Metrics

# Value at Risk (VaR)
# Expected Shortfall
# Correlation breakdown scenarios
# Systemic risk indicators

Applications

• Portfolio optimization
• Risk management
• Algorithmic trading
• Market microstructure
• Crisis prediction
• Cryptocurrencies

Fat-Tailed Distributions

# Lévy stable distributions
from scipy.stats import levy_stable
# Student-t for returns
# Power law for极端 events