Based on P245 of [[complete guide to capital markets]]

Discount curve is designed to tells us how to discount to NPV $1 received x days from today, where x can be 1 to 365 * 30. If the curve value for Day 365 is 0.80, then SPOT rate is 25% or 2500bps — 80 cents invested today becomes $1. Note the value on the curve is not bps or spot rate, but a discount factor value from 0 to 1.

Q: how do I get forward rate between any 2 dates?

A: P246. Simple formula.

Discount curve is “built” from and must be consistent with

+ ED CD rates (spot rates) of 1,7,14..,90 days. As loans, these loan term always starts today.

+ ED futures rates (forward rates). Loan term always last 3 months, but start on the 4 IMM dates of this year, next year, next next year ….

(Note ED futures rates are determined on the market; ED CD rates are announced by BBA.)

(Note I have ignored IR swaps, which are more liquid than ED futures beyond 10Y tenor.)

Discount curve needs to cover every single date. First couple of months are covered by latest announced ED CD rates, interpolating when necessary. After we pass 90, all subsequent dates (up to 30 years) are covered by ED futures rates observed on CME. Being forward rates, these aren’t directly usable as those CD rates, but still very simple — If the 3-month forward rate 3/19/2008 – 6/19/2008 is 200bps, and discount factor for 3/19 is 0.9, then 6/19 discount factor is (0.9 / 1.02)