Fixed-Income Analytics

A bond is the most honest instrument in finance: a written promise to pay you fixed cash on fixed dates. That honesty is exactly what makes it so analytically rich — because the cash flows are pinned down, the price is pure discounting, the risk is pure calculus, and a single market number, the yield, ties the whole thing together. Master that, and you can price a trillion-dollar government market, run a pension’s liabilities, or hedge a bond desk down to the last basis point.

This is the expert continuation of Bonds & Rates. You already know what a bond is and why its price moves opposite to yields; here you learn to quantify every bit of that, the way a rates trader, a fixed-income PM, or a risk manager does:

• Bond pricing math — turn a stream of coupons plus a face value into a present value, define yield to maturity precisely, and see why price and yield are locked in an inverse, convex dance.
• Duration — Macaulay duration as the cash-flow balance point, modified duration as the price’s percentage sensitivity to yield, and DV01 as the dollar bleed per basis point.
• Convexity — the second-order correction that fixes duration’s straight-line lie, and why convexity is a free gift to the bondholder.
• Bootstrapping the yield curve — strip coupon bonds into pure spot (zero) rates, then extract the forward rates the market has priced for the future, all by no-arbitrage.
• Term-structure models — a first quantitative look at Vasicek and CIR: short rates that mean-revert on a leash, the bridge into stochastic processes.
• Credit spreads & default risk — decompose a risky yield into the risk-free rate, the expected loss (default probability × loss given default), and the risk premium that pays you to bear uncertainty.
• Immunization & hedging — match duration (and convexity) to a liability so a rate move barely scratches your surplus, and compute the DV01 hedge ratio that neutralizes a whole book.

By the end you’ll price a bond from scratch, measure its sensitivity three different ways, build the curve the market trades off, price the cost of default, and hedge a rate book like a desk. From here the ladder climbs into stochastic processes, where the mean-reverting short rate you meet in Vasicek becomes a fully-fledged random process.