Credit Rating Migration Analysis Project Overview This project implements a quantitative analysis of credit rating migrations using Markov chain methodology. The code simulates how a portfolio of corporate bonds transitions between different credit rating categories over time, including the probability of default.
Key Features Transition Matrix Visualization: Heatmap representation of one-year credit rating transition probabilities
Portfolio Projection: Multi-year projection of portfolio composition using matrix exponentiation
Default Risk Analysis: Tracking of migration to default state over time
Professional Visualizations: Clean, publication-ready charts using Matplotlib and Seaborn
Methodology
- Markov Chain Framework The analysis uses a discrete-time Markov chain where:
States: AAA, AA, A, BBB, BB, B, CCC, Default (absorbing state)
Transition Matrix: Row-stochastic matrix P where P[i,j] = probability of moving from state i to state j in one year
Absorbing State: Default state has probability 1 of remaining in default
- Mathematical Foundations Portfolio Distribution: v₀ = initial portfolio vector
k-year Distribution: vₖ = v₀ × Pᵏ
Matrix Exponentiation: Pᵏ computed using np.linalg.matrix_power(P, k)
Data Structure Transition Matrix The 8×8 transition matrix includes:
Rows: Starting credit rating
Columns: Ending credit rating after one year
Properties:
Each row sums to 1 (probability conservation)
Default state row: [0, 0, 0, 0, 0, 0, 0, 1]
Higher ratings show greater stability (diagonal dominance)
Initial Portfolio text Initial Portfolio (Millions USD): AAA: $100M AA: $150M A: $200M BBB: $250M BB: $150M B: $100M CCC: $50M Default: $0M Total: $1B Code Components Main Functions project_portfolio_df(v0, P, max_years)
Projects portfolio distribution for specified years
Returns DataFrame with year-by-year rating composition
Uses matrix exponentiation for multi-year projections
Visualization Functions
Heatmap of transition probabilities
Stacked bar chart of portfolio evolution
Separate tracking of default accumulation
Dependencies python numpy==1.24.0 # Matrix operations and numerical computations pandas==2.0.0 # Data structures and DataFrame manipulation matplotlib==3.7.0 # Basic plotting and chart creation seaborn==0.12.0 # Enhanced visualization (heatmap styling) Output Visualizations
- Transition Matrix Heatmap Color-coded probability matrix (YlGnBu colormap)
Annotated with probability values (4 decimal places)
Clear axis labels for starting/ending ratings
- Portfolio Projection Chart Stacked bar chart showing rating migration over 5 years
Separate visualization of default accumulation
Spectral colormap for non-default states
Gray bars for default values
Key Insights Risk Migration Patterns Investment Grade Stability: AAA-AAA transitions show highest stability (90.81%)
Default Risk Concentration: Lower ratings (CCC) show significant default probability (20.19% in one year)
Portfolio Deterioration: Over 5 years, portfolio migrates toward lower ratings
Default Accumulation: Defaulted assets accumulate in absorbing state
Business Applications Credit Risk Management: Estimate portfolio deterioration over time
Regulatory Capital: Calculate expected losses for Basel compliance
Investment Strategy: Assess risk-return tradeoffs in bond portfolios
Stress Testing: Simulate adverse migration scenarios
Usage Instructions Basic Execution python
python credit_migration_analysis.py Customization Options Modify initial portfolio:
python initial_portfolio_values = { 'AAA': your_value, 'AA': your_value, ... } Adjust projection horizon:
python max_projection_years = 10 # Extend to 10 years Update transition matrix:
python P = np.array([...]) # Replace with proprietary transition data Assumptions and Limitations Model Assumptions Time Homogeneity: Transition probabilities constant over time
Markov Property: Future rating depends only on current rating
Discrete Time: Annual transition intervals
Stationary Process: No macroeconomic cycle effects
Limitations Historical Bias: Based on historical data, may not predict future
Rating Agency Dependence: Uses agency ratings, not market-implied
Correlation Ignored: No inter-asset dependency modeling
Liquidity Effects: No consideration of market liquidity on ratings
Extensions and Future Work Potential Enhancements Multi-period Transitions: Incorporate economic cycle-dependent matrices
Monte Carlo Simulation: Add stochastic elements for VaR calculation
Recovery Rates: Include loss given default (LGD) parameters
Sector Analysis: Different transition matrices by industry sector
Regulatory Reporting: Generate Basel III compliant output formats
Research Applications Compare agency ratings vs. market-implied ratings
Test rating momentum vs. mean reversion hypotheses
Analyze transition matrix stability across business cycles