FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"
A delta-neutral, long-gamma option position is held for one day with no rebalancing. Ignoring theta, which statement best describes the expected effect of a large move in the underlying price?
The position gains in either direction. With delta zero, profit is roughly half of gamma times the squared price change, which is positive when gamma is positive, so large moves up or down help, though theta is the cost.
- AThe position gains whether the price rises or fallsCorrect
- BThe position loses whether the price rises or falls
- CThe position gains only if the price rises
- DThe position gains only if the price falls
Explanation
With zero delta, the P&L is approximately 0.5 x gamma x (change in S)^2, which is positive for positive gamma regardless of direction. In practice this gain is paid for through time decay (theta).
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