Structured Credit Products (CDOs and Securitizations) › Worked Example: Analyzing a \$500M CDO
Michael BrenndoerferNovember 19, 20254 min read
Quantitative FinanceAll chapters Part 4 of 15Swaps and Credit Derivatives
Structured Credit Products (CDOs and Securitizations) › Worked Example: Analyzing a \$500M CDOOne section · Sections in this chapter8 / 12 ↓
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Let's work through a complete example of a cash CDO backed by 100 corporate loans.
In[29]:
Code# CDO Parameters
pool_size = 500_000_000 # $500 million
n_loans = 100
loan_size = pool_size / n_loans
avg_default_prob = 0.04 # 4% annual default probability
recovery_rate = 0.40
correlation = 0.25
# Tranche structure
# Defined with explicit attachment/detachment to ensure consistency
cdo_tranches = {
"Senior": {"coupon": 0.015, "attachment": 0.12, "detachment": 1.00},
"Mezzanine A": {"coupon": 0.04, "attachment": 0.07, "detachment": 0.12},
"Mezzanine B": {"coupon": 0.07, "attachment": 0.04, "detachment": 0.07},
"Equity": {"coupon": 0.0, "attachment": 0.00, "detachment": 0.04},
}
# Calculate notionals
for name, spec in cdo_tranches.items():
thickness = spec["detachment"] - spec["attachment"]
spec["notional"] = thickness * pool_sizeIn[30]:
Code# Run Monte Carlo simulation for 5-year horizon
n_simulations = 100000
years = 5
cumulative_default_prob = (
1 - (1 - avg_default_prob) ** years
) # ~18.5% over 5 years
defaults = simulate_correlated_defaults(
n_loans, cumulative_default_prob, correlation, n_simulations
)
pool_losses = (defaults / n_loans) * (
1 - recovery_rate
) # Loss rate after recovery
# Calculate tranche metrics
tranche_metrics = []
for name, spec in cdo_tranches.items():
attach = spec["attachment"]
detach = spec["detachment"]
thickness = detach - attach
# Tranche losses
tranche_loss_rates = np.clip(pool_losses - attach, 0, thickness) / thickness
# Expected loss
expected_loss = tranche_loss_rates.mean()
# Probability of any loss
prob_any_loss = (tranche_loss_rates > 0).mean()
# Probability of total loss
prob_total_loss = (tranche_loss_rates >= 0.999).mean()
tranche_metrics.append(
{
"Tranche": name,
"Notional ($M)": spec["notional"] / 1e6,
"Attachment": f"{attach * 100:.0f}%",
"Detachment": f"{detach * 100:.0f}%",
"Expected Loss (%)": expected_loss * 100,
"P(Any Loss)": prob_any_loss,
"P(Total Loss)": prob_total_loss,
}
)
metrics_df = pd.DataFrame(tranche_metrics)Out[31]:
ConsoleCDO Tranche Analysis - 5 Year Horizon
================================================================================
Pool Size: $500M | Loans: 100 | Correlation: 0.25
5-Year Default Prob: 18.5% | Recovery: 40%
--------------------------------------------------------------------------------
Tranche Notional ($M) Attachment Detachment Expected Loss (%) P(Any Loss) P(Total Loss)
Senior 440.0 12% 100% 3.471 0.360 0.000
Mezzanine A 25.0 7% 12% 47.829 0.604 0.383
Mezzanine B 15.0 4% 7% 68.445 0.779 0.604
Equity 20.0 0% 4% 89.172 0.983 0.779The simulation results quantify the risk segmentation. The Equity tranche, while offering potential upside, faces a high probability of total loss (approx. 60%). In contrast, the Senior tranche remains untouched in the vast majority of scenarios, protected by the subordination of the lower tranches.
Out[32]:
Visualization
