Solution: Derivatives of Core Finance Functions

Exercise: Derivatives of Core Finance Functions

Solution

The derivatives are $nS^{n-1}$, $-re^{-rt}$, and $1/S$. They appear in power payoffs, discount factors, and log-return calculations respectively.

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.