FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"
A portfolio of options on an index has delta of 12,000, gamma of -800 (per $1 change in the index level) and theta of 0 over the horizon considered. Using a delta-gamma Taylor approximation, what is the estimated change in portfolio value if the index rises by $5?
The estimated change is a gain of $50,000. The delta term contributes $60,000 (12,000 times 5), and the gamma term subtracts $10,000 (half of 800 times 25), giving a net of $50,000.
- A$50,000Correct
- B$60,000
- C$70,000
- D$40,000
Explanation
Change = delta x dS + 0.5 x gamma x dS^2 = 12,000 x 5 + 0.5 x (-800) x 25 = 60,000 - 10,000 = 50,000. The $60,000 option ignores the gamma term. The $70,000 option gets the sign of the gamma term wrong.
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