Curves
A curve turns a date into a number: a discount factor, a survival probability, a spread or an index level. Here you'll find each kind of curve, what it stores, how it reads between the dates it was given, and what it remembers about where it came from. Most curves in practice are marked from a quote sheet, as the market shows; the pages here build each kind directly, because the curve itself is their subject.
Where to start
- How curves work explains the ideas every curve page relies on.
- Discount curves builds a curve from discount factors and from one rate.
- Reading a curve shows what a curve answers.
- Interpolation shows what happens between the pillars.
- The other kinds, step, spread, repo spread, survival, inflation and parametric curves, build on discount curves, reading and interpolation.
- Provenance shows what a solved curve remembers.
Pages
| Page | What it covers |
|---|---|
| how-curves-work | explanation: what each kind of curve is for, and reading rates off factors by hand |
| discount-curves | factors at pillars, extrapolation past the last, a flat curve |
| reading-a-curve | discount factors, zero rates and forwards; the rate day count |
| interpolation | explanation: schemes as values; agreement at pillars; flat forwards against splines |
| step-curves | knots on decision dates and turns; flat forwards between knots |
| spread-curves | a security's spread, flat or dated, over its currency's curve |
| repo-spread-curves | GC and specials as simple spreads chained over a base |
| survival-curves | survival from pillars, a hazard or a default density; credit identity and recovery |
| inflation-curves | index levels, linear or log-linear, and seasonality |
| parametric-fits | a Nelson-Siegel curve fitted to bonds; its natural parameters and misfits |
| provenance | explanation: the ladder a solved curve carries, and a bare curve's lack of one |
Common tasks
| You want to | Go to |
|---|---|
| read a zero rate or a forward off a curve | reading-a-curve |
| choose how a curve interpolates | interpolation |
| build a curve from your own rungs | build a curve from your own rungs |
| price a swap on a curve you marked | price a swap from today's quotes |
| report a book's DV01 and par ladder | Report a book's risk |
From the 0.0 line at revision bf7f2e2. Every printed number is that revision's own output.