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

The current one-year rate is 5%. In one year the one-year rate will be 6% (up) or 4% (down), each with risk-neutral probability 0.5. A European call expires in one year on a zero-coupon bond that matures in two years, face value 100, with a strike price of 95. What is the call's value today?

The call is worth about 0.55. At expiry the underlying bond is worth 94.34 or 96.15, so the call pays 0 or 1.15. The risk-neutral expected payoff of 0.577 is discounted one period at the 5% short rate to give 0.549.

  1. A0.55Correct
  2. B0.58
  3. C1.10
  4. D0.00

Explanation

At expiry the bond is worth 100/1.06 = 94.34 in the up state and 100/1.04 = 96.15 in the 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, or about 0.55. Omitting the discounting gives 0.58, and omitting the probability weight gives 1.10.

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