Credit Default Swap (CDS) Calculator
Bootstrap a hazard-rate and survival-probability curve from CDS spreads with the reduced-form model. Reprice the swaps and check default probabilities instantly.
Credit Default Swap Hazard Rate Calculator
A clear path from inputs to results.
Turn quoted credit default swap (CDS) spreads into a default-probability curve, and check that curve by re-pricing the swaps. It uses the market-standard reduced-form approach: a piecewise-constant hazard (default-intensity) rate is bootstrapped so the premium leg and protection leg have equal present value. It is aimed at credit analysts and students learning survival-based pricing.
How to use
- Set the recovery rate R, the fraction of face value expected to be recovered after a default; the loss given default is 1 - R.
- Set the risk-free discount rate used to present-value both legs of the swap.
- Set the premium payment step (in years) — a quarterly step (0.25) matches standard CDS coupon frequency and makes the leg integrals finer.
- Set the flat initial hazard used as a fallback starting guess for the bootstrap solver.
- Choose the horizon (years) for how far the survival-probability curve is plotted; the model calibrates to the built-in 1/3/5/7/10-year market spread quotes.
- Read the bootstrapped hazard term structure, the survival-probability curve, and the comparison of model par spreads against the market spreads to confirm the fit.
The formula
Reference: O'Kane, D. & Turnbull, S. (2003), "Valuation of Credit Default Swaps," Lehman Brothers Fixed Income Quantitative Research; ISDA Standard CDS Model (reduced-form hazard-rate pricing).
Worked example
Bootstrapping the credit curve from the default spread quotes
- Recovery R = 0.4; discount rate = 0.03; payment step = 0.25 years; flat initial hazard = 0.025. Market CDS spreads: 1Y 80 bps, 3Y 120 bps, 5Y 160 bps, 7Y 210 bps, 10Y 260 bps.
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The solver bisects on each maturity bucket in turn so the protection leg (1-R)*sum D(t)[S(t_prev)-S(t)] equals the premium leg s*sum dt*D(t)*S(t). This yields piecewise-constant hazards of 1.3311% (0-1y), 2.3527% (1-3y), 3.8093% (3-5y), 6.1382% (5-7y) and 7.2617% (7-10y). Integrating the hazard gives survival probabilities S(1) = 0.986777, S(5) = 0.872361 and S(10) = 0.620539. Re-pricing a 5-year CDS off this curve returns a par spread of exactly 1.600%, matching the 160 bps input. As a sanity check, the average hazard to 5 years is -ln(0.872361)/5 = 2.730%, and the credit-triangle approximation (1-R)*hazard = 0.6*2.730% = 1.638% is close to the 160 bps quote.
A rising hazard curve from 1.33% (1Y) to 7.26% (10Y), a 5-year survival probability of 0.872361 (about a 12.8% cumulative default chance), and model par spreads that reprice the market quotes exactly.
Interpreting the result
The hazard rate is the instantaneous, conditional probability of defaulting in the next instant given survival so far; the survival curve S(t) is its cumulative effect. An upward-sloping hazard curve (as here) means the market prices rising conditional default risk further out. Because each hazard bucket is solved to reprice its spread quote, the "model vs market spread" lines should overlap — any gap flags a calibration or input problem. The recovery rate matters a lot: holding spreads fixed, a lower R implies lower hazards because each default costs more.
Assumptions & limitations
- The market spread quotes and maturity grid are built into the tool (1/3/5/7/10 years at 80-260 bps); you calibrate recovery, discounting and schedule to them rather than entering your own quotes.
- Hazard rates are piecewise-constant between the quoted maturities, so the curve is a step function rather than a smooth intensity.
- Default and interest rates are assumed independent, and the discount curve is a single flat rate rather than a full risk-free term structure.
- Recovery is a fixed fraction known in advance; it does not vary with the state of the economy or the timing of default.
- Accrued premium on default and precise ISDA day-count/business-day conventions are simplified relative to a production CDS pricer.
Frequently asked questions
What is a hazard rate in CDS pricing?
The hazard rate (default intensity) lambda is the instantaneous rate of default conditional on having survived so far. Over a short interval dt the conditional default probability is roughly lambda*dt, and the survival probability is S(t) = exp(-integral of lambda). The reduced-form approach treats default as the first jump of this intensity process.
Why is the fair CDS spread approximately (1 - R) times the hazard rate?
This is the "credit triangle." Ignoring discounting and timing, the annual expected loss is (1-R)*lambda and the premium you pay is the spread s, so s ~ (1-R)*lambda. With a 2.730% average hazard to 5 years and R = 0.4, that gives (1-R)*lambda = 1.638%, close to the 160 bps quote. The solver does the exact present-value calculation instead of this shortcut.
What does the 5-year survival probability of 0.872 mean?
It means the model implies about an 87.2% chance the reference entity survives the full five years without a credit event, and therefore roughly a 12.8% cumulative probability of default over that horizon. These are risk-neutral probabilities implied by market prices, which are generally higher than real-world (physical) default probabilities.
How does bootstrapping the hazard curve work?
Starting from the shortest maturity, the tool finds the constant hazard over that bucket that makes the CDS price fairly (protection-leg PV equals premium-leg PV at the quoted spread), then moves to the next maturity holding earlier buckets fixed, and so on. This piecewise calibration reproduces every quoted spread, which is why the model and market spread lines coincide.
How does the recovery rate affect the result?
The protection leg pays (1 - R) of notional on default, so a lower recovery means each default is more costly. To match the same market spread, the implied hazard rate must be lower when R is lower, and higher when R is higher. Recovery is therefore a critical and often debated input; 40% is a common senior-unsecured convention.
Are these risk-neutral or real-world default probabilities?
Risk-neutral. They are extracted from traded CDS spreads, which embed a risk premium investors demand for bearing default risk. Real-world default frequencies estimated from rating agencies or historical data are typically lower. Use the risk-neutral curve for pricing and hedging, not as a direct forecast of actual default rates.
Methodology last reviewed 2026-10-06. Results are informational and not financial or engineering advice — see our disclaimer.