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7.3 Computation of the arbitrage-free value of an option-free, fixed-rate coupon bond

For option-free bonds, the simplest approach to arbitrage-free valuation involves determining the arbitrage-free value as the sum of the present values of expected future values using the benchmark spot rates. Benchmark securities are liquid, safe securities whose yields serve as building blocks for other interest rates in a particular country or currency.

General formula:

( )

( )

( )

where z1, z2, zNare the spot rates for period 1, 2, and N.

  • Sovereign debt is the benchmark in many countries.

Example. Assume an option-free bond with four years to maturity and an annual coupon of 6.5%.

Year Spot Rate One-Year Forward Rate 1 3.5000% 3.500% 2 4.215% 4.935% 3 4.735% 5.784% 4 5.271% 6.893% V + + + V + + +

Lesson Wrap-Up

This lesson should leave you able to explain the computation of the arbitrage-free value of an option-free, fixed-rate coupon bond in a fixed-income context and connect it to the decisions made by issuers, investors, or analysts.

Review Prompts

  1. Explain computation of the arbitrage-free value of an option-free, fixed-rate coupon bond in your own words.
  2. State one exam-style risk, valuation, or market implication of the computation of the arbitrage-free value of an option-free, fixed-rate coupon bond.