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FRM Part II · FRM Exam Part II · Arbitrage Pricing with Term Structure Models

In a one-period binomial interest rate tree, a zero-coupon bond with face value 100 matures next period. The current one-period rate is 4% (annual compounding, one-year step). The rate next period is either 5% or 3% (not needed for this bond's payoff). A one-year zero-coupon bond pays 100 for sure. What is its price today?

The price is 96.15. A certain payoff of 100 in one year is discounted at the known one-year rate of 4%, giving 100/1.04. The up and down rates next period are irrelevant because the bond's payoff is fixed and not state dependent.

  1. A96.15Correct
  2. B95.24
  3. C104.00
  4. D97.09

Explanation

A one-year zero pays 100 with certainty, so its price is 100/1.04 = 96.15 regardless of the risk-neutral probability. Discounting at 5% gives 95.24, which uses the wrong rate; 97.09 uses 3%. Multiplying by 1.04 gives 104.00, which compounds instead of discounting.

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