Yield Curve Bootstrapping

Every rate on every swap, bond and derivative is ultimately a read from a curve. Before you can price anything, you need to understand exactly how that curve is built — not as a black box, but as a sequence of explicit steps you can verify, stress and trust. This course walks you through the full construction process from first principles.

You will build two curves that professional desks use in tandem: an OIS discount curve, stripped from overnight-indexed swap quotes using sequential root-finding, and a SOFR 3M forward curve, anchored to CME futures prices. Both are interpolated with cubic splines fitted to log-discount factors, which guarantees positive forward rates and smooth curve shapes.

By the end you will understand day-count conventions deeply enough to spot a convention mismatch in the wild, you will know exactly why OIS and SOFR curves diverge, and you will have a dual-curve pricer that correctly discounts with the OIS curve while projecting SOFR forwards — the industry-standard post-LIBOR setup.

The project is a self-contained Python library for building and querying a rates curve. You start with raw market data: a short-end money-market deposit, a series of OIS swap quotes at standard tenors, and a strip of SOFR 3M futures prices. Your first task is to implement the three main day-count conventions — Act/360, Act/365 and 30/360 — correctly enough to replicate exchange-quoted year fractions to the day.

With the foundations in place you implement the OIS bootstrap: for each tenor, you solve for the discount factor that prices the OIS swap at par, conditioning on all shorter-dated factors already solved. You then extend the curve to the IMM futures dates using SOFR futures prices, and interpolate both curves using a cubic spline on the logarithm of the discount factors, which is the interpolation method used by most professional curve engines.

The final deliverable is a dual-curve pricer: given a fixed-for-floating swap, you value it by projecting cash flows with the SOFR forward curve and discounting them with the OIS discount curve. You then stress the curve with parallel and key-rate shifts and observe the sensitivity of par swap rates and DV01 — the exact workflow a rates quant uses to build and validate a new curve.