Bootstrapping

Bootstrapping is the standard method for deriving the zero-coupon (spot) rate curve from observed par yields. It works iteratively, starting from the shortest maturity and solving for each successive spot rate.

The logic is straightforward: a coupon bond can be viewed as a portfolio of zero-coupon cash flows. Since we know the bond's price (par, by definition for par rates) and the discount rates for all earlier cash flows (from prior bootstrap steps), we can solve for the remaining unknown — the spot rate at that maturity.

The procedure:

1. The shortest maturity par rate equals the spot rate (only one cash flow)
2. For each subsequent maturity, discount all intermediate coupons at the already-known spot rates, then solve for the final spot rate that makes the present value of all cash flows equal to par
3. Repeat until the entire spot curve is built

Once the spot curve is known, forward rates can be extracted directly from the relationship between any two spot rates.

Bootstrapping is one of the foundational techniques in fixed-income analytics. The Salomon Brothers yield curve primer (Part 1) provides a detailed walkthrough, and the method remains the standard approach used by dealers, risk systems, and analytics platforms to construct zero curves from market data.