FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"
A portfolio of options on a stock has a delta of 0.20 and a gamma of 0.05 (per $1 move in the stock). The stock price rises by $2. Using a delta-gamma approximation, what is the approximate change in portfolio value?
The delta-gamma approximation gives 0.20 × 2 plus one-half × 0.05 × 2 squared, which is 0.40 plus 0.10, or $0.50. Delta alone gives only $0.40 because it ignores the convexity adjustment from gamma.
- A$0.40
- B$0.50
- C$0.60Correct
- D$0.90
Explanation
Change = delta × ΔS + 0.5 × gamma × (ΔS)² = 0.20×2 + 0.5×0.05×4 = 0.40 + 0.10 = 0.50. Check: that gives 0.50, so the correct value is $0.50. Using delta alone gives $0.40, which omits the convexity term.
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