Term Structure — Spot, Forward, Bootstrapping & Swap Curves

Learning objectives

By the end you can:

1. Explain the chicken-and-egg problem that makes bootstrapping necessary, why the market's directly-quoted par yields cannot, by themselves, correctly price anything the curve was not built from.
2. Bootstrap a spot (zero) curve from a set of on-the-run par/coupon bonds (India G-Secs and US Treasuries) using linear interpolation of the sparse par curve followed by sequential discount-factor solving, and prove it by discounting every input bond's own cash flows back through the curve and confirming an exact reprice to par.
3. Compute implied forward rates from a spot curve via the no-arbitrage identity, and prove numerically that investing directly at a longer spot rate produces the identical terminal value as rolling at the shorter spot rate and then the implied forward rate.
4. Price an off-the-run bond off a bootstrapped spot curve, solve for its yield to maturity, and explain (with a worked number, not just a rule) why that YTM generally differs from the par yield quoted at the same maturity (the coupon effect).
5. State the expectations, liquidity-premium, and market-segmentation/preferred-habitat theories of the term structure in quantitative (algebraic) form, as decompositions of the forward rate, building explicitly on the narrative version of these theories already taught in M7.03.
6. Bootstrap a swap curve (INR OIS/MIBOR or USD SOFR) from par swap rates, having first proved (via the floating-rate-note-at-par argument) why the identical bond-bootstrap algorithm applies; then compute and correctly interpret a swap spread, distinguishing it explicitly from a corporate credit spread (E11.01).
7. Build and calibrate, as a deliberate sketch, a one-factor short-rate model (Vasicek); compare its model-implied curve to the empirical bootstrap; and state precisely what a short-rate model buys you that a static bootstrap cannot.
8. Apply India (on-the-run G-Secs, FBIL/CCIL/FIMMDA conventions, SDLs, INR OIS/MIBOR) and US (on-the-run UST, SOFR) market conventions correctly, and never confuse the curve-*shape*/inversion-signal skill (M7.03) with the curve-*construction* skill taught here.
9. (Productivity objective: R10 duality.) Use AI to accelerate drafting or debugging a bootstrapping script, or to explain a formula, while treating the reprice-and-roll-forward proof as the one non-negotiable verification step that no AI-produced curve, spread, or model fit is ever exempt from.

Prerequisites & connections

Builds on. FI1.01 (Bond Pricing & Yield Measures) is assumed fluent: YTM, current yield, and the money-market yield conversions are inputs to this module, not review; this module builds the curve that FI1.01's single-bond pricing takes as given. FI1.02 (Duration, Convexity & Interest-Rate Risk) is referenced, never re-taught: Macaulay/modified duration, PVBP/DV01, and key-rate duration all operate on the spot curve this module constructs, and a key-rate duration is literally "bump one point of this curve and reprice", but the mechanics of duration itself live in FI1.02, not here. M1.08 (Liabilities & Financing) §4.1 teaches bond accounting, amortized cost under the effective-interest method, the book-value roll-forward a company reports on its balance sheet. That is a different object from what this module does: M1.08 answers "what does the issuer's book say this liability is worth," carried at a historical effective rate; this module answers "what does the market say a cash flow landing at time t is worth today," off a curve that is re-built from current quotes every day. Never let the two blur into each other. M7.03 §4.10–§4.13 already introduced the yield curve's shape (normal/flat/inverted/humped), the inversion-as-recession-signal, the expectations-plus-term-premium decomposition of a long spot yield, the liquidity-preference and market-segmentation/preferred-habitat theories by name, and the duration formula. This module is the deliberate quantitative complement: it does not re-derive any of that narrative, it builds the machinery, the bootstrap, the forward-rate algebra, and the same three theories extended algebraically to the forward curve, that turns M7.03's shapes into priced numbers. E11.01 §11.2 established corporate yield = risk-free rate + credit spread; this module's swap-spread section leans on that scaffold explicitly and then shows why a swap spread is not a credit spread in E11.01's sense.