The money market does not trade zero-coupon bonds at every maturity. Instead, rates are observable from three overlapping instrument classes: money-market deposits (LIBOR/SOFR fixings) for maturities up to 12 months, interest rate futures for the one-to-two-year window, and swap rates for two to thirty years. Bootstrapping extracts implied discount factors from this overlapping data, one maturity at a time, building the curve from the short end out.
The method is the workhorse of every rates desk. It exactly reprices every input instrument and is fast enough to run in real time. Its weakness is a jagged forward curve — the linear interpolation of swap rates that the method implicitly assumes creates discontinuities in implied forward rates. Parametric curve families trade away exact fit for smoothness.
Learning objectives. By the end of this note you should be able to:
- state the general term-structure estimation problem as ;
- extract zero-coupon bond prices from money-market rates using the simple compounding formula;
- use futures prices to extend the curve beyond the money-market window, including linear interpolation at overlapping maturities;
- extract discount factors at swap maturities by solving the swap pricing equation recursively;
- explain the convexity adjustment that distinguishes futures rates from forward rates;
- identify the "sawtooth" problem in implied forward rates and explain its source.
In this lesson
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- The general estimation problem
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- The money-market segment
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- The futures segment
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- The swap segment
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- The sawtooth problem
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- Cash-flow matrix perspective
Before you start
- Zero-Coupon Bonds, Market Rates, Swaps, and Conventions
- Bond Prices, Discount Factors, and the Law of One Price
The full lesson, with worked examples and exercise solutions, is for members.
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