FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"
Consider four European calls on the same non-dividend-paying stock and the same strike structure. Which call is likely to have the largest absolute sensitivity (rho) to a change in the risk-free rate?
The 3-year deep in-the-money call has the largest rho. Rho equals K T e^(-rT) N(d2), so it rises with maturity and with the probability term N(d2), which is close to one for a deep in-the-money option.
- AA 3-year call that is deep in the moneyCorrect
- BA 1-month call that is deep out of the money
- CA 1-year at-the-money call
- DA 3-year call that is deep out of the money
Explanation
Rho = K T e^(-rT) N(d2). It grows with maturity T. It also grows with N(d2), which is near 1 for a deep in-the-money call and near 0 for a deep out-of-the-money call. The 3-year deep in-the-money call combines the largest T with N(d2) near 1.
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