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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 strike K = 100, maturity T = 2 years and a continuously compounded risk-free rate of 5%. The model gives N(d2) = 0.55. Using e^(-0.10) = 0.9048, approximately how much does the call price change if the risk-free rate rises by one percentage point?

The call price rises by about 0.995. Rho equals K times T times e^(-rT) times N(d2), which is 100 × 2 × 0.9048 × 0.55 = 99.53 per unit change in rate, so a 0.01 rate increase adds roughly 0.995.

  1. AIncrease of about 0.995Correct
  2. BIncrease of about 1.10
  3. CIncrease of about 0.498
  4. DIncrease of about 1.81

Explanation

Rho = K T e^(-rT) N(d2) = 100 × 2 × 0.9048 × 0.55 = 99.53 per 1.00 change in rate. A one percentage point rise is 0.01, so the price change is about 0.995. 1.10 omits the discount factor. 0.498 omits T. 1.81 omits N(d2).

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