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FRM Part I · FRM Exam Part I · Properties of Options

An American call on a non-dividend-paying stock is priced at 4.00. The stock price is 31, the strike is 30, expiry is three months, and the continuously compounded risk-free rate is 10%. Which range correctly bounds the price of the American put with the same strike and expiry?

The American put must lie between 2.26 and 3.00. For American options on a non-dividend stock, S0 - K ≤ C - P ≤ S0 - PV(K). Rearranging with C = 4 gives a lower bound of 4 - 31 + 29.26 = 2.26 and an upper bound of 4 - 31 + 30 = 3.00.

  1. A2.26 to 3.00Correct
  2. B2.26 to 4.00
  3. C0.74 to 2.26
  4. D3.00 to 4.74

Explanation

For American options on a non-dividend stock, S0 - K ≤ C - P ≤ S0 - K e^(-rT). With K e^(-0.025) = 29.26: P ≥ C - S0 + K e^(-rT) = 4 - 31 + 29.26 = 2.26, and P ≤ C - S0 + K = 4 - 31 + 30 = 3.00. The other ranges mix up the bounds or the signs.

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