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docs: add 6 comprehensive example files for v7.0.0 modules
- 08_credit_risk.py: Merton model, CDS pricing/bootstrap, portfolio EL/UL/credit VaR, Z-spread - 09_volatility_models.py: 5 OHLCV estimators, GARCH/GJR fit+forecast, HAR-RV, regimes - 10_monte_carlo.py: GBM, Heston, jump-diffusion, CIR, option pricing vs BS benchmark - 11_portfolio_insurance.py: CPPI bull/bear/sensitivity, TIPP ratcheting floor - 12_benchmark_analytics.py: IR/TE/capture, active share, BHB sector attribution - 13_scenario_analysis.py: 9 historical scenarios, custom shocks, reverse stress, corr stress - examples/README.md: updated index and learning path
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‎examples/08_credit_risk.py‎

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"""
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Example 08: Credit Risk Analysis
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Demonstrates MeridianAlgo's credit risk module:
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- Merton structural model: equity as call option on firm assets
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- Default probability term structure
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- CDS pricing and hazard rate bootstrapping
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- Portfolio expected loss and credit VaR
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- Z-spread and DV01 computation
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"""
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import numpy as np
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import pandas as pd
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from meridianalgo.credit import (
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CreditDefaultSwap,
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CreditRiskAnalyzer,
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MertonModel,
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ZSpreadCalculator,
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)
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# ---------------------------------------------------------------------------
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# 1. Merton Structural Model
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# ---------------------------------------------------------------------------
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print("=" * 60)
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print("1. MERTON STRUCTURAL MODEL")
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print("=" * 60)
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# A leveraged firm: $500M equity, $800M debt, 35% equity vol
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model = MertonModel(
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equity_value=500e6,
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equity_volatility=0.35,
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debt_face_value=800e6,
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time_to_maturity=1.0,
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risk_free_rate=0.05,
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)
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result = model.calibrate()
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print(f"Input equity value: ${500e6/1e6:.0f}M")
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print(f"Input debt face value: ${800e6/1e6:.0f}M")
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print(f"Input equity vol: 35.00%")
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print()
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print(f"Implied asset value: ${result['asset_value']/1e6:.1f}M")
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print(f"Implied asset vol: {result['asset_volatility']:.2%}")
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print(f"Leverage ratio: {result['leverage_ratio']:.2%}")
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print(f"Distance to default: {result['distance_to_default']:.4f} sigma")
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print(f"Default probability: {result['default_probability']:.4%}")
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print(f"Expected recovery rate: {result['expected_recovery_rate']:.4%}")
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# Compare three firms: low, medium, and high leverage
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print("\n--- Leverage Comparison ---")
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firms = [
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("Low leverage", 800e6, 0.25, 200e6),
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("Medium leverage", 500e6, 0.35, 800e6),
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("High leverage", 200e6, 0.50, 1500e6),
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]
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for name, equity, ev, debt in firms:
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m = MertonModel(equity, ev, debt, time_to_maturity=1.0, risk_free_rate=0.05)
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r = m.calibrate()
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print(f" {name:20s} DD={r['distance_to_default']:6.3f} PD={r['default_probability']:.4%}")
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# ---------------------------------------------------------------------------
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# 2. Default Probability Term Structure
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# ---------------------------------------------------------------------------
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print("\n" + "=" * 60)
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print("2. DEFAULT PROBABILITY TERM STRUCTURE")
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print("=" * 60)
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model_ts = MertonModel(
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equity_value=400e6,
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equity_volatility=0.40,
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debt_face_value=900e6,
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time_to_maturity=1.0,
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risk_free_rate=0.05,
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)
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horizons = [0.25, 0.5, 1.0, 2.0, 3.0, 5.0, 7.0, 10.0]
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term_struct = model_ts.default_probability_term_structure(horizons)
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print(f"{'Horizon':>10} {'PD':>10} {'Annualized':>12}")
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for t, pd_val in term_struct.items():
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ann_pd = 1 - (1 - pd_val) ** (1 / t) if t > 0 else 0
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print(f"{t:>10.2f} {pd_val:>10.4%} {ann_pd:>12.4%}")
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# ---------------------------------------------------------------------------
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# 3. CDS Pricing
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# ---------------------------------------------------------------------------
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print("\n" + "=" * 60)
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print("3. CDS PRICING")
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print("=" * 60)
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# Constant hazard rate CDS
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cds = CreditDefaultSwap(
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hazard_rate=0.02,
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recovery_rate=0.40,
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risk_free_rate=0.05,
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maturity=5.0,
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payment_frequency=4,
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)
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r = cds.price()
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print(f"Hazard rate: {cds.hazard_rate:.4f}")
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print(f"Recovery rate: {cds.recovery_rate:.2%}")
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print(f"Fair spread: {r.fair_spread * 10000:.2f} bps")
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print(f"Risky annuity (DV01): {r.risky_annuity:.6f}")
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print(f"5yr survival prob: {r.survival_probability:.6f}")
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# Spread sensitivity to hazard rate
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print("\n--- Spread vs Hazard Rate ---")
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print(f"{'Hazard Rate':>14} {'5yr Spread (bps)':>18} {'5yr Survival':>14}")
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for h in [0.005, 0.010, 0.020, 0.040, 0.080, 0.150]:
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c = CreditDefaultSwap(h, recovery_rate=0.40, maturity=5.0)
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r = c.price()
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print(f" {h:12.3%} {r.fair_spread * 10000:>16.2f} {r.survival_probability:>14.6f}")
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# Recover hazard rate from market spread
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print("\n--- Bootstrap Hazard Rate from Market Spread ---")
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market_spread = 0.0180
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cds_from_spread = CreditDefaultSwap.from_spread(
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spread=market_spread,
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recovery_rate=0.40,
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risk_free_rate=0.05,
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maturity=5.0,
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)
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print(f"Market spread: {market_spread * 10000:.1f} bps")
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print(f"Implied hazard: {cds_from_spread.hazard_rate:.6f}")
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check = cds_from_spread.price().fair_spread
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print(f"Verified spread: {check * 10000:.2f} bps (roundtrip error: {abs(check - market_spread)*1e6:.1f} micro-bps)")
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# Bootstrap full hazard curve
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print("\n--- CDS Curve Bootstrap ---")
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maturities = [1.0, 3.0, 5.0, 7.0, 10.0]
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market_spreads = [0.0080, 0.0120, 0.0150, 0.0175, 0.0210]
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hazard_curve = CreditDefaultSwap.bootstrap_hazard_curve(
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maturities, market_spreads, recovery_rate=0.40, risk_free_rate=0.05
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)
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print(f"{'Maturity':>10} {'Market Spread':>16} {'Hazard Rate':>14}")
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for mat, spread, hazard in zip(maturities, market_spreads, hazard_curve.values):
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print(f" {mat:8.1f}y {spread * 10000:>14.1f}bps {hazard:>14.6f}")
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# ---------------------------------------------------------------------------
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# 4. Portfolio Credit Risk: EL, UL, Credit VaR
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# ---------------------------------------------------------------------------
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print("\n" + "=" * 60)
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print("4. PORTFOLIO CREDIT RISK")
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print("=" * 60)
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analyzer = CreditRiskAnalyzer()
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# Loan portfolio
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portfolio = pd.DataFrame({
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"obligor": ["Corp A", "Corp B", "Corp C", "Corp D", "Corp E",
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"Corp F", "Corp G", "Corp H"],
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"rating": ["BBB", "BB", "B", "BBB", "A",
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"BB", "CCC", "A"],
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"pd": [0.0020, 0.0080, 0.0250, 0.0020, 0.0005,
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0.0080, 0.1000, 0.0005],
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"lgd": [0.45, 0.50, 0.60, 0.40, 0.35,
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0.50, 0.70, 0.35],
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"ead": [5e6, 3e6, 1e6, 8e6, 10e6,
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2e6, 0.5e6, 15e6],
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})
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portfolio["el"] = portfolio.apply(
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lambda r: analyzer.expected_loss(r["pd"], r["lgd"], r["ead"]), axis=1
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)
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portfolio["ul"] = portfolio.apply(
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lambda r: analyzer.unexpected_loss(r["pd"], r["lgd"], r["ead"]), axis=1
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)
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portfolio["credit_var_99"] = portfolio.apply(
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lambda r: analyzer.credit_var(r["pd"], r["lgd"], r["ead"], confidence=0.999), axis=1
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)
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print(portfolio[["obligor", "rating", "pd", "lgd", "ead", "el", "credit_var_99"]]
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.to_string(index=False, float_format=lambda x: f"{x:,.0f}" if x > 100 else f"{x:.4f}"))
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result = analyzer.portfolio_expected_loss(portfolio[["pd", "lgd", "ead"]])
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print(f"\nPortfolio Summary:")
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print(f" Total EAD: ${portfolio['ead'].sum()/1e6:.1f}M")
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print(f" Total Expected Loss: ${result['total_el']/1e3:.1f}K ({result['el_rate']:.3%} of EAD)")
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print(f" Total Unexpected Loss: ${result['total_ul']/1e3:.1f}K")
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print(f" Herfindahl Index: {result['herfindahl_index']:.4f}")
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print(f" Top-10 Concentration: {result['top10_concentration']:.2%}")
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# ---------------------------------------------------------------------------
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# 5. Z-Spread and DV01
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# ---------------------------------------------------------------------------
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print("\n" + "=" * 60)
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print("5. Z-SPREAD AND DV01")
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print("=" * 60)
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# 5% coupon bond, 5-year maturity
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cash_flows = [50, 50, 50, 50, 1050]
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times = [1.0, 2.0, 3.0, 4.0, 5.0]
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risk_free_rates = [0.035, 0.038, 0.040, 0.042, 0.044]
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calc = ZSpreadCalculator(cash_flows, times, risk_free_rates)
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par_price = calc.theoretical_price(0.0)
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print(f"Risk-free par price: ${par_price:.4f}")
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market_prices = [par_price - 5, par_price - 2, par_price, par_price + 2, par_price + 5]
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print(f"\n{'Market Price':>14} {'Z-Spread (bps)':>16} {'DV01':>10}")
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for price in market_prices:
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z = calc.z_spread(price)
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dv01 = calc.dv01(z)
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print(f" ${price:10.4f} {z * 10000:>14.2f} {dv01:>10.4f}")
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print(f"\nDV01 at z=0: {calc.dv01():.4f} (approx ${calc.dv01() * 1000:,.2f} per $1M notional per bp)")

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