Yield Curve Bootstrapping
Use a sequence of traded rates to solve for discount factors and build a zero-coupon curve.
Bootstrapping starts from the shortest-maturity instruments and works forward in time.
At each maturity it uses known discount factors from earlier pillars to solve for the next discount factor.
The result is a set of zero-coupon rates and discount factors consistent with observed par yields.
This graphic shows three quoted par yields and the bootstrapped zero-coupon curve. Bootstrapping solves for discount factors sequentially so that all bond prices are exactly matched.
The grey dashed line is the par curve you observe in the market. Bootstrapping uses the 1Y instrument to pin down D(1Y), then uses that discount factor to solve the 2Y bond equation for D(2Y), and so on.
The blue line is the zero curve implied by these discount factors. In an upward-sloping environment, zero rates tend to sit below par rates at the same maturity, because coupons are partly paid earlier at lower discount rates. The key mental model: you are turning a small set of traded yields into a full set of discount factors that pricing models can use consistently.