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Financial Instruments, Markets and Conventions / Fixed Income: Bonds, Yields, and Interest Rate Risk

Zero-Coupon and Coupon Bonds: Cash Flows, Pricing, and the Discount-Factor Framework

A bond is the simplest possible derivative: it is a contract that obligates the issuer to pay a specified sequence of cash flows — periodic coupons and a lump-sum principal at maturity — to the holder. The bond's price is the present value of that sequence, discounted at the rate the market demands for the issuer's credit quality and the bond's maturity. Every fixed-income concept in this topic — yield to maturity, duration, convexity, the zero curve — is a further elaboration of this single valuation equation.

Understanding bond pricing precisely matters because the discount rates used to value bonds — the zero-coupon rates extracted from the Treasury market — are the same rates used to value interest rate swaps, forward rate agreements, and every other rate-sensitive instrument in the unit. The bond market is the zero curve, and the zero curve is the discount engine for all interest-rate derivatives.
Learning objectives. By the end of this note you should be able to:
  • describe the cash flows of an option-free coupon bond and a zero-coupon bond;
  • price a coupon bond given a single yield-to-maturity using the full bond pricing formula;
  • price a coupon bond as a portfolio of zero-coupon bonds discounted at maturity-specific zero rates;
  • identify whether a bond is at a discount, par, or premium from its coupon rate and required yield;
  • explain the pull-to-par effect and the three reasons a bond's price changes over time;
  • calculate accrued interest using the actual/actual (Treasury) and 30/360 (corporate) conventions and distinguish the clean price from the dirty price (full price);
  • interpret the discount-factor framework and explain why a coupon bond equals a portfolio of zero-coupon bonds.

In this lesson

  1. Anatomy of a bond
  2. The bond pricing formula
  3. The price-yield relationship
  4. The discount-factor framework
  5. Price quotes and accrued interest

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