Overview — The Term Structure of Interest Rates

This topic covers the term structure from the market data up: what the instruments are, how to extract discount factors from them (bootstrapping), how to fit smooth parametric models to noisy data (Nelson-Siegel, Svensson, B-splines), what the principal components of historical curve movements look like, and what the term-structure slope tells us about the market's expectations of future rates and the risk premium embedded in the long end.

By the end of this topic you should be able to:

• define the zero-coupon bond $P(t,T)$, the spot rate $R(t,T)$, the instantaneous forward rate $f(t,T)$, and the short rate $r(t)$, and state the exact algebraic relationships among them;
• price a coupon bond, a floating rate note, and an interest rate swap from discount factors;
• bootstrap a term structure from a mix of money-market rates, futures prices, and swap rates;
• explain the trade-off between exact fit (non-parametric) and smooth curves (parametric) and when each is appropriate;
• parameterise the Nelson-Siegel forward curve and interpret its four parameters as level, slope, and curvature;
• decompose historical forward-curve changes into three principal components and name their market interpretations;
• state the expectations hypothesis, identify the convexity adjustment, and explain the risk premium in the term premium.

1. Contents
2. The big picture