Lesson 2 of 6 · All lessons in this module
  1. Spot rates and the spot curve
  2. Pricing a bond with spot ratesVideo lesson
  3. Par rates and the par curveVideo lesson
  4. Implied forward rates from spot ratesVideo lesson
  5. Spot rates from forward rates, and pricing with forwardsVideo lesson
  6. Comparing the spot, par and forward curves

Lesson 2 of 6 · 13 min

Pricing a bond with spot rates

Discount each cash flow at the spot rate for its own date: the sum is the bond's no-arbitrage price, and the YTM is just the single rate that gives the same total.

In short

  • A coupon bond is a bundle of zeros, so each cash flow is discounted at the spot rate for its date: PV=PMT(1+Z1)+PMT(1+Z2)2+⋯+PMT+FV(1+ZN)NPV = \frac{PMT}{(1+Z_1)} + \frac{PMT}{(1+Z_2)^2} + \dots + \frac{PMT+FV}{(1+Z_N)^N}.
  • The result is the no-arbitrage price. If the market price differs, an arbitrage exists (ignoring transaction costs).
  • The YTM is the one rate that reproduces that price. The PV of each single cash flow differs between the two methods, but the totals match.
  • On an upward-sloping curve, a coupon bond's YTM is slightly below the spot rate for its maturity.
  • For a riskier bond (for example a corporate), add a spread to each spot rate.

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