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:

• A: $1.287 (too low)
• B: $1.291 (closest to $1.28735)
• C: $1.295 (too high)

Therefore, $1.291 is the closest estimate.