Explanation:
To estimate the new option price using delta and gamma:
First-order approximation (delta only):
Price change = Delta × Underlying price change = 0.40 × $0.70 = $0.28
Second-order approximation (delta + gamma):
Price change = (Delta × Underlying price change) + (0.5 × Gamma × (Underlying price change)²)
= (0.40 × $0.70) + (0.5 × 0.03 × ($0.70)²)
= $0.28 + (0.5 × 0.03 × $0.49)
= $0.28 + (0.5 × 0.0147)
= $0.28 + $0.00735
= $0.28735
New estimated price:
Original price + Price change = $1.00 + $0.28735 = $1.28735
Among the options:
$1.287 (too low)$1.291 (closest to $1.28735)$1.295 (too high)Therefore, $1.291 is the closest estimate.
An option has an original price of $1.00, a delta of 0.40 and a gamma of 0.03. Ignoring the effect of volatility, if the underlying's price changes by $0.70, the estimated new price of the option would be closest to:
A
$1.287
B
$1.291
C
$1.295
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