econophysics

## 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 ```python # Correlation matrix analysis import numpy as np # Eigenvalue spectrum (Marchenko-Pastur) # Random matrix theory filtering # Minimum spanning tree networks ``` ### Risk Metrics ```python # 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 ```python # Lévy stable distributions from scipy.stats import levy_stable # Student-t for returns # Power law for极端 events ```