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

Two European call options on the same non-dividend-paying stock are identical except for maturity: one expires in 1 month, the other in 1 year. Both are at-the-money. Which statement about their vegas is correct?

The 1-year at-the-money call has the higher vega. Vega rises with time to maturity, roughly with the square root of time, because volatility has longer to influence the distribution of the terminal price. The 1-month option has higher gamma, not higher vega.

  1. AThe 1-year call has the higher vega because more time allows volatility to affect the terminal price distributionCorrect
  2. BThe 1-month call has the higher vega because it has higher gamma
  3. CBoth have the same vega since they share the same strike
  4. DNeither has vega because at-the-money options are insensitive to volatility

Explanation

For at-the-money options, vega increases with time to maturity, roughly in proportion to the square root of time. Short-dated at-the-money options have higher gamma but lower vega. Strike alone does not determine vega.

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