Term Structure of Interest Rates › Summary

This chapter covered the fundamental concepts underlying fixed-income analysis and yield curve construction:

Zero rates and discount factors are the basis for valuing any fixed-income security. The zero rate for maturity $T$ tells you the rate of return for an investment from today until $T$ with no intermediate cash flows. The corresponding discount factor $D(T) = e^{-z(T) \cdot T}$ gives the present value of receiving $1 at time $T$.

Forward rates represent the rates implied by the spot curve for future borrowing or lending. They can be computed from zero rates using the no-arbitrage relationship, but interpreting them as forecasts requires assumptions about term premia. For strictly increasing continuously compounded zero rates, a later interval forward rate exceeds the zero rate at its endpoint; the initial interval forward equals its corresponding zero rate.

Bootstrapping is a standard technique to extract zero rates from coupon bond prices. Proceeding from short to long maturities uses solved nodes and an explicit interpolation rule for missing coupon dates. If those intermediate rates depend on the new node, solve the coupled pricing equation rather than treating every coupon discount as already fixed.

Yield-curve shapes convey economic information without uniquely identifying its cause. An upward curve can reflect rising expected rates or a positive term premium. Inversions of selected US Treasury spreads have historically preceded recessions, with sample-specific lead times and false positives. Flat or humped shapes can arise from different expected-rate paths, premia or supply and demand.

These tools support bond pricing, interest-rate derivative valuation and rate-risk measurement. A useful next step is to reprice each calibration instrument with the resulting discounts and check that the residuals are small under the stated conventions.