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

A bank has sold a call option on 100,000 shares of a non-dividend-paying stock and hedges it with a static (not rebalanced) delta hedge established at inception. Which statement best describes the hedge's effectiveness over time?

The hedge deteriorates as the stock price moves. Option delta changes with the underlying price (gamma) and over time, so a share position set at inception no longer offsets the option exposure, and the shares have zero gamma, so rebalancing is needed.

  1. AIt stays perfect because delta is constant for a European call
  2. BIt deteriorates as the stock price moves, because delta changes with the price and timeCorrect
  3. CIt improves as the stock moves further from the strike, only if volatility rises
  4. DIt is unaffected by gamma because gamma is hedged by the shares

Explanation

Delta changes with the stock price (gamma) and with time, so a hedge set once becomes mismatched and requires rebalancing. Shares have zero gamma, so they cannot hedge gamma risk; delta is not constant for a call.

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