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

A risk analyst builds a one-period binomial tree for the short rate. The current one-period rate is 4.00%. After one period the rate is either 5.00% or 3.00% with equal risk-neutral probabilities. Using this tree, what is the price of a two-period zero-coupon bond with face value 100, discounting at the tree rates (annual compounding)?

The price is about 92.45. Discount the face value 100 back one period at each node (95.24 and 97.09), average them under equal risk-neutral probabilities to get 96.16, then discount one more period at 4.00%, giving roughly 92.46.

  1. A92.30
  2. B92.45Correct
  3. C92.59
  4. D92.08

Explanation

Time-1 values: 100/1.05 = 95.2381 and 100/1.03 = 97.0874. Expected value = 96.1628. Discount at 4%: 96.1628/1.04 = 92.4642, which rounds to 92.46, closest to 92.45. Discounting 100 at a flat 4% for two periods gives 92.46 as well, so the key is the tree value; 92.59 results from discounting 100/1.04^2 mistakenly using 3.9% and is wrong.

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