Solution: Delta-Gamma Approximation for Option P&L

Exercise: Delta-Gamma Approximation for Option P&L

Solution

The delta-only estimate is $0.55(-3)=-1.65$. The second-order estimate is $-1.65+\frac{1}{2}(0.04)(9)-0.02=-1.49$. Gamma matters because it scales with the square of the move.

Takeaways

• The derivative or Taylor coefficient has a direct P&L interpretation once the units are named.
• The common mistake is to treat a local sensitivity as an exact large-move statement.