Michael Brenndoerfer | Data & AI, Private Equity, Technology

Michael Brenndoerfer

Credit Default Swaps (CDS) and Credit Derivatives › Implied Default Probability from CDS Spreads

Michael BrenndoerferNovember 18, 20254 min read

Quantitative FinanceAll chapters

Part 4 of 15Swaps and Credit Derivatives

Chapter 22Credit Default Swaps (CDS) and Credit Derivatives › Implied Default Probability from CDS Spreads

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CDS spreads provide market-based estimates of default probability. Given an observed spread, we can back out the implied hazard rate using our pricing formula. This "implied probability" represents the market's consensus view of credit risk, incorporating all available information about the reference entity as processed by thousands of market participants.

The approximation $s \approx \lambda(1-R)$ gives us:

\lambda_{\text{implied}} \approx \frac{s}{1-R}

where:

$\lambda_{\text{implied}}$ : hazard rate implied by market prices
$s$ : observed market CDS spread
$R$ : assumed recovery rate

The implied hazard rate depends on your recovery rate assumption. If you assume 40% recovery, a 120 bps spread implies a 2% hazard rate. But if you assume 20% recovery, the same spread implies only a 1.5% hazard rate. You must be careful to state your recovery assumptions when discussing implied default probabilities.

In[29]:

Code

import numpy as np

# Extract implied default probabilities from market CDS spreads
observed_spreads_bps = np.array(
    [50, 100, 200, 300, 500, 1000]
)  # Market spreads
recovery_assumption = 0.40

# Implied hazard rates
implied_hazard_rates = (observed_spreads_bps / 10000) / (
    1 - recovery_assumption
)

# 5-year cumulative default probabilities
implied_5y_default_prob = 1 - np.exp(-implied_hazard_rates * 5)

Out[30]:

Console

Implied Default Probabilities from CDS Spreads
------------------------------------------------------------
  CDS Spread (bps)       Implied λ    5Y Default Prob
------------------------------------------------------------
                50          0.83%             4.08%
               100          1.67%             8.00%
               200          3.33%            15.35%
               300          5.00%            22.12%
               500          8.33%            34.08%
              1000         16.67%            56.54%

These implied probabilities provide valuable information about market perceptions of credit risk. A CDS spread of 200 bps implies roughly a 15% probability of default over five years, while 1000 bps (10%) indicates the market sees default as quite likely.

In[31]:

Code

# Calculate ranges for plotting
spread_range = np.linspace(10, 1500, 100)
hazard_range = (spread_range / 10000) / (1 - recovery_assumption)
default_prob_range = 1 - np.exp(-hazard_range * 5)

Out[32]:

Visualization

Line chart showing implied default probability increasing with CDS spread. — Implied 5-year cumulative default probabilities derived from CDS spreads assuming 40% recovery. The relationship is non-linear, showing that as spreads cross the 1,000 basis point threshold, the implied probability of default over five years exceeds 55%.

The curve demonstrates that as CDS spreads widen, the implied default probability increases non-linearly. This convexity means that for high-yield entities, even small spread movements imply significant changes in the market's perception of default risk.

Out[33]:

Visualization

Line chart showing implied 5-year default probability versus CDS spread for three recovery rate assumptions of 20%, 40%, and 60%. — Implied default probability curves for varying recovery rate assumptions (20%, 40%, 60%). The chart demonstrates that for a fixed CDS spread, assuming a higher recovery rate necessitates a higher implied default probability to maintain the same expected loss equivalence.