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

A one-period tree has a short rate of 4% (annual compounding). A zero-coupon bond maturing at the end of period two is priced today from a tree where next-period rates are 6% (up) and 2% (down), with risk-neutral probability 0.5 each. The bond pays 100 at the end of period two. What is its price today?

Roll back the tree: average the two node values using risk-neutral probabilities, then discount at 4%, giving about 92.49.

  1. A92.46Correct
  2. B92.59
  3. C92.45
  4. D92.32

Explanation

Value at the node after one period: up = 100/1.06 = 94.340; down = 100/1.02 = 98.039. Expected = 0.5*94.340 + 0.5*98.039 = 96.189. Discount at 1.04: 96.189/1.04 = 92.49. This differs from the key, so the closest listed value is 92.46 is inexact; the correct computed value is about 92.49.

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