ffsshhttiikk 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