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

A risk analyst models the one-year short rate with a binomial tree. The current one-year rate is 5%. One year from now the one-year rate will be either 6% or 4%, each with a risk-neutral probability of 0.5. Using annual compounding and backward induction, what is the value today of a two-year zero-coupon bond with face value 100?

The bond is worth about 90.71. Its year-1 values are 94.34 and 96.15, averaging 95.25 under equal risk-neutral probabilities, and this expected value is then discounted one further year at the current 5% short rate.

  1. A89.86
  2. B90.71Correct
  3. C91.58
  4. D95.25

Explanation

At year 1 the bond is worth 100/1.06 = 94.3396 in the up state and 100/1.04 = 96.1538 in the down state. The risk-neutral expectation is 95.2467. Discounting one more period at 5% gives 90.71. Stopping at 95.25 omits the first-period discount, which is the key error.

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