CDS Term Structure: Bootstrapping the Survival Curve

A flat hazard rate is a useful teaching device, but it is not how the market prices credit risk. Observed CDS spreads vary by maturity — a 1Y CDS and a 10Y CDS on the same issuer almost never imply the same hazard rate — and any serious credit analytics system must respect that term structure. This course shows you how to calibrate a piecewise-constant hazard rate model to the full CDS curve using the same sequential bootstrap that underlies industry standard tools.

The bootstrap algorithm is elegant: solve for the hazard rate in the first pillar by requiring that the 1Y CDS NPV is zero at the quoted spread, then lock it in and solve for the next pillar against the 2Y CDS quote, and so on out to 10Y. Each step is a single one-dimensional root-finding problem, and the result is a survival curve that is internally consistent with every quoted CDS maturity. The course derives the algorithm from the CDS pricing equations you already know and implements it cleanly in Python.

Beyond bootstrapping, the course covers the quantities that practitioners use every day: forward CDS spreads (the spread on a CDS starting in the future), default probability densities, expected losses, and scenario analysis under parallel curve shifts. It also covers the mark-to-market of seasoned trades against the new curve — the calculation that hits your P&L every time the curve moves. By the end you have a complete, production-grade survival curve engine.

You begin with a CDS term structure — par spreads quoted at 1Y, 2Y, 3Y, 5Y, 7Y and 10Y — and a SOFR-based risk-free curve. The first stage is to verify the flat-hazard-rate case: using the credit triangle, confirm that the single constant hazard rate implied by each maturity differs across the curve, demonstrating why a term structure model is necessary.

The main stage is the sequential bootstrap. You implement a root-finder loop that processes each CDS maturity in order: given all previously calibrated hazard rates (which are now fixed), solve for the hazard rate in the current interval such that the full CDS NPV — protection leg minus premium leg, using the exact integral pricing from the CDS pricing course — is zero at the quoted par spread. You bootstrap all six pillars and store the resulting piecewise-constant λ(t) curve.

In the final stage you use the bootstrapped survival curve to compute forward CDS spreads (the break-even spread on a forward-starting CDS), the default probability density q(t), and expected loss EL(T) as a function of horizon. You then stress the curve with a parallel spread shift, reprice a seasoned CDS trade, and compute the P&L impact. The completed engine is wrapped into a reusable Python class with a clean API for pricing and scenario analysis.