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

Use the same tree: the one-year rate is 5% today and becomes 6% or 4% at year 1 with risk-neutral probabilities of 0.5 each. A European call option expires at year 1 on a two-year zero-coupon bond (face 100, so it has one year left at expiry) with a strike of 95. What is the option's value today?

The call is worth about 0.55. Only the down-rate state, where the bond is worth 96.15, pays off 1.15. Weighting by 0.5 gives 0.58, and discounting one year at the 5% short rate gives 0.55.

  1. A0.55Correct
  2. B0.58
  3. C1.10
  4. D1.15

Explanation

At expiry the bond is worth 94.3396 (up state) and 96.1538 (down state). The call pays 0 in the up state and 1.1538 in the down state. The expected payoff is 0.5769, and discounting at 5% gives 0.5494, about 0.55. Omitting the discount gives 0.58.

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