Work out the arbitrage-free value of a straight fixed-coupon bond
The idea
Value an option-free, fixed-rate bond by discounting each cash flow at the spot rate for its own date and adding the results: coupon ÷ (1 + S₁) + coupon ÷ (1 + S₂)² and so on, with the final cash flow including principal. Spot rates can come directly from strip prices or be bootstrapped from the par curve. The same answer comes from discounting through successive forward rates. A bond whose coupon exceeds the relevant spot rates trades above par. The frequent mistake is discounting every cash flow at a single rate, such as the longest spot rate or another bond's yield, instead of using the matching spot rate for each date.
In the app: 2 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
Take the free diagnostic →More in The Arbitrage-Free Valuation Framework
- Explain the idea of valuing a fixed-income instrument so that no arbitrage is possible
- Explain the framework of a binomial tree for interest rates
- Explain how a binomial interest rate tree is calibrated so that it fits a given term structure
- Explain valuation by backward induction, and use it to value a fixed-income instrument from its cash flow at every node
- Contrast valuing with the zero-coupon yield curve and valuing with an arbitrage-free binomial lattice
- Explain pathwise valuation within a binomial interest rate model, and use it to value a fixed-income instrument from its cash flows on every path
- Explain how a Monte Carlo simulation of forward rates works and where it is applied
- Explain term structure models and the uses they are put to