TRADING CASE B05
Zero-coupon bonds and a trinomial interest-rate tree
LEARNING OBJECTIVE
Value short-maturity zero-coupon bonds using the possible paths of one-month spot rates.
KEY CONCEPTS
Term structure of interest rates | Interest-rate risk | Unbiased expectations | Risk premium

EVOLUTION OF ONE-MONTH SPOT RATES

MONTH 1MONTH 2MONTH 36.5%11.0%9.0%5.0%18.609%15.232%12.468%8.462%6.927%3.848%

Monthly rates are not annualized. Month 2 outcomes are equally likely.

HOW THE CASE WORKS

Three zero-coupon bonds mature in one, two, and three months. Trading occurs on the first day of each month. After each session, time advances, cash interest is settled, and any maturing bond pays 100.

VALUATION DYNAMICS

The one-month bond uses the current spot rate. Longer bonds depend on future branches in the tree. Work backward from maturity; market prices may also reflect a risk premium.

BOND CASH FLOWS

BondMonth 1Month 2Month 3
GKO-110000
GKO-201000
GKO-300100

Borrowing and short sales are permitted. Students determine prices through bids and asks.