FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"
A call option has delta 0.60 and gamma 0.04 per dollar. The stock rises by 2 dollars. Using a delta-gamma approximation, what is the approximate change in the call price?
The approximate price change is 1.28. Delta contributes 0.60 x 2 = 1.20, and the gamma adjustment adds 0.5 x 0.04 x 2 squared = 0.08, giving a total increase of 1.28.
- A1.28Correct
- B1.20
- C1.36
- D0.08
Explanation
Change = delta x dS + 0.5 x gamma x dS^2 = 0.60 x 2 + 0.5 x 0.04 x 4 = 1.20 + 0.08 = 1.28. Using delta alone gives 1.20; subtracting the gamma term gives 1.12; doubling it incorrectly gives 1.36.
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