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

A one-period-ahead binomial tree for the annual short rate has a current rate of 4%. After one year the rate is either 8% or 2%, with risk-neutral probabilities of 50% each. Rates are compounded annually. What is the arbitrage-free price of a two-year zero-coupon bond with face value 100?

The price is 91.65. Discount 100 back one year in each state, giving 92.59 and 98.04, take the 50/50 risk-neutral average of 95.32, then discount at the current 4% rate. Discounting at the average future rate gives 91.58 and ignores convexity.

  1. A91.65Correct
  2. B91.58
  3. C89.03
  4. D94.27

Explanation

Work backward. The year-1 bond value is 100/1.08 = 92.5926 in the up state and 100/1.02 = 98.0392 in the down state. The risk-neutral expectation is 95.3159, and discounting at 4% gives 91.65. Option 91.58 discounts at the average rate of 5% rather than averaging bond prices, so it ignores convexity. The other two options use only one state.

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