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

A two-year bond pays a 6% annual coupon on a face value of 100 and is callable at par (100, ex-coupon) by the issuer at t=1, immediately after the first coupon. The one-year rate is 5% today and will be 7% or 3% at t=1, each with risk-neutral probability 0.5. Assuming the issuer calls optimally, what is the bond's value today?

The callable bond is worth about 100.51. The issuer calls only in the down-rate state, capping the ex-coupon value at 100 instead of 102.91. Adding the coupon gives 105.07 and 106, an average of 105.53, which is discounted at 5%. The non-callable bond is worth 101.89.

  1. A100.51Correct
  2. B101.89
  3. C97.65
  4. D99.93

Explanation

At t=1, ex-coupon, the uncalled value is 106/1.07 = 99.065 (up) and 106/1.03 = 102.913 (down). The issuer calls only in the down state, so that value is capped at 100. Adding the 6 coupon gives 105.065 and 106. The average is 105.533, and discounting at 5% gives 100.51. The non-callable value is 101.89. 97.65 results from capping the coupon-inclusive value at 100.

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