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

A trader holds European options on a non-dividend-paying stock and considers the effect of a small parallel rise in the risk-free rate, with all other inputs held constant. Which statement is correct?

The call gains and the put loses. A higher risk-free rate reduces the present value of the strike price. The call holder pays the strike, so benefits, while the put holder receives it, so loses. Hence call rho is positive and put rho is negative for European options on non-dividend stocks.

  1. ABoth the call and the put gain value, because higher rates raise the forward price of the stock.
  2. BThe call gains value and the put loses value, because rho is positive for calls and negative for puts.Correct
  3. CThe call loses value and the put gains value, because a higher discount rate lowers the present value of the call's payoff.
  4. DBoth the call and the put lose value, because the present value of the strike falls for both.

Explanation

A higher rate lowers the present value of the strike. That helps the call holder, who pays the strike, and hurts the put holder, who receives it. So call rho is positive and put rho is negative. The claim that both lose value ignores the opposite direction of strike effects on the two positions.

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