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

A risk analyst uses a one-period-recombining binomial tree for the annualised one-year rate. The current one-year rate is 4.00%. After one year the rate is either 7.00% or 3.00%, each with risk-neutral probability 0.5. Annual compounding applies. What is the model price of a two-year zero-coupon bond with face value 100?

The price is 91.61. Work backwards through the tree: value the bond at each year-1 node (93.46 and 97.09), take the risk-neutral expectation (95.27), then discount one period at the current 4% rate. Averaging rates first would give a slightly different, incorrect value.

  1. A91.61Correct
  2. B92.46
  3. C91.58
  4. D95.27

Explanation

At year 1 the bond is a one-year zero: 100/1.07 = 93.4579 in the up state and 100/1.03 = 97.0874 in the down state. The expected value is 95.2727, and discounting at 4% gives 91.61. Discounting at 4% for both years gives 92.46 and ignores the rate uncertainty. Using 4% then 5% gives 91.58, which discounts the average rate rather than averaging the prices.

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