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

A bank has sold a call option and delta-hedged it. Which statement best describes the hedged position's result if the stock makes a large move in either direction before the hedge is rebalanced?

The delta-hedged short call loses money on a large move in either direction because it carries negative gamma. Delta neutrality protects only against small price changes, so the curvature of the option payoff creates losses before rebalancing.

  1. AIt loses money because the position has negative gammaCorrect
  2. BIt gains money because the position has negative gamma
  3. CIt gains money because the position has positive vega
  4. DIt is unaffected because delta is zero

Explanation

A short option position has negative gamma. A delta hedge only protects against small moves, so a large move in either direction produces a loss from the convexity mismatch. Zero delta does not remove gamma exposure.

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