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

A trader holds a long position in a European call option on a non-dividend-paying stock. All else equal, which statement best describes the option's theta as the option moves from at-the-money towards deep out-of-the-money?

Theta for a long call is negative because time value erodes toward expiry. The erosion is largest near at-the-money, where time value is greatest, and diminishes for deep out-of-the-money options, whose value is already small and has little left to lose.

  1. ATheta is typically negative for the long call, and its absolute size is largest near at-the-money and shrinks as the option moves deep out-of-the-moneyCorrect
  2. BTheta is positive for the long call because time value increases as expiry nears
  3. CTheta is zero for all calls on non-dividend-paying stocks
  4. DTheta becomes more negative the further the option moves out-of-the-money

Explanation

A long call on a non-dividend stock loses time value as expiry approaches, so theta is negative. The decay per day is greatest when the option is near the money, where time value is highest, and falls toward zero for deep out-of-the-money options. The option claiming theta grows more negative further out-of-the-money has the pattern reversed.

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