Solution: First-Order P&L of a Stock Position

Exercise: First-Order P&L of a Stock Position

Solution

The derivative is $q$, so $\Delta V\approx q\Delta S$. Since $V$ is linear in $S$, all higher derivatives vanish and the first-order Taylor approximation is exact.

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.