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FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"

A European call and a European put on the same non-dividend-paying stock share strike K = 80 and maturity T = 2 years. The continuously compounded risk-free rate is 3%. The call's rho is 90.41 per 1.00 change in the rate (e^(-0.06) = 0.941765). Using put-call parity, what is the put's rho on the same basis?

The put's rho is -60.27. Differentiating put-call parity with respect to the rate shows that call rho minus put rho equals strike times maturity times the discount factor, which is 150.68. Subtracting that from the call's 90.41 gives a negative put rho of -60.27.

  1. A-60.27Correct
  2. B+60.27
  3. C-241.09
  4. D-90.41

Explanation

Parity gives rho_call - rho_put = K·T·e^(-rT) = 80 × 2 × 0.941765 = 150.68. So rho_put = 90.41 - 150.68 = -60.27. The +60.27 option has the wrong sign, and -241.09 comes from adding the call rho instead of subtracting it.

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