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

A non-dividend-paying stock trades at 50. An American call and an American put each have a strike of 50 and six months to expiry. The call price is 4.00 and the continuously compounded risk-free rate is 4%. Using the put-call relationships for American options, with exp(-0.02) = 0.980199, between what bounds must the American put price lie?

The American put must lie between 3.01 and 4.00. The lower bound is the European parity value, 4 - 50 + 49.01. The upper bound is C - S0 + K = 4, because early exercise rights can make the American put worth more than its European counterpart.

  1. ABetween 3.01 and 4.00Correct
  2. BExactly 3.01
  3. CBetween 0 and 3.01
  4. DBetween 4.00 and 4.99

Explanation

For American options on a non-dividend stock, S0 - K <= C - P <= S0 - K*exp(-rT). With S0 = K = 50, Ke^(-rT) = 49.0099, so 0 <= 4 - P <= 0.9901. The upper bound on P comes from 4 - P >= 0, giving P <= 4.00. The lower bound comes from 4 - P <= 0.9901, giving P >= 3.01. The value 3.01 is the European put price only, and early exercise rights can add value up to 4.00.

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