Credit Default Swaps: Pricing from First Principles

The credit default swap is the central instrument of the credit derivatives market, yet most practitioners who use CDS — for hedging, speculation or index trading — could not price one from first principles. This course builds that understanding from the ground up. You derive the protection and premium legs as integrals over the survival curve, write the closed-form expressions, and turn them into a working Python pricer.

The 2009 ISDA Big Bang changed how CDS trades. Standard coupons of 100 bps and 500 bps replaced running-spread quotes, and upfront payments became the norm. Most introductory treatments still describe the pre-2009 world. This course teaches the modern market convention first, derives the upfront formula from the fundamental pricing equation, and shows you how to convert between par spread and upfront using the risky annuity.

Beyond single-name pricing the course covers the key sensitivities — CS01 (credit sensitivity) and IR01 (rate sensitivity) — and their applications in hedging. It also covers seasoned CDS mark-to-market and intrinsic CDX index valuation, so by the end you have the toolkit to think rigorously about credit risk across the most liquid instruments in the market.

The project begins with a flat hazard rate and an OIS discount curve. You first implement the protection leg — the expected present value of the loss given default — as a numerical integral over the term structure of default probability, correctly handling the recovery rate and discounting. You then implement the premium leg under the ISDA accrual convention, which accounts for the partial coupon accrued when default occurs mid-period.

With both legs in place you derive the par spread formula (protection PV equals premium PV at par) and the risky PV01 — also called the risky annuity or RPVBP — which is the dollar sensitivity of the premium leg to a one-basis-point change in running spread. You then implement the post-2009 upfront convention: given a standard coupon (100 bps or 500 bps) and a par spread, solve for the upfront payment using the RPVBP, and verify the round-trip conversion.

In the final stage you compute a CS01 term structure — the sensitivity of each instrument in a CDS portfolio to a one-basis-point shift in the hazard rate at each maturity — and an IR01 (the sensitivity to a parallel shift in the risk-free curve). You then price a CDX index as the intrinsic spread (the notional-weighted average of its single-name constituents), discuss index basis, and wrap the entire pricer into a clean, reusable Python module.