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

A European call on a non-dividend-paying stock has K = 90 and T = 1.5 years. The risk-free rate is 4% continuously compounded, with e^(-0.06) = 0.9418. The call has a rho of 80 per 1.00 change in the interest rate. What is the rho of the European put with the same strike and maturity, per 1.00 change in the rate?

The put rho is about -47.1. Differentiating put-call parity shows call rho minus put rho equals K T e^(-rT) = 90 × 1.5 × 0.9418 = 127.14, so the put rho is 80 minus 127.14, which is -47.14.

  1. AAbout -47.1Correct
  2. BAbout +47.1
  3. CAbout -127.1
  4. DAbout +207.1

Explanation

Put-call parity gives c - p = S - K e^(-rT). Differentiating with respect to r gives rho_call - rho_put = K T e^(-rT) = 90 × 1.5 × 0.9418 = 127.14. So rho_put = 80 - 127.14 = -47.14. +47.1 has the sign wrong. -127.1 ignores the call rho. +207.1 adds instead of subtracts.

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