Solution: Call Payoff Kink and Delta

Exercise: Call Payoff Kink and Delta

Solution

For $S<K$, $C(S)=0$ so the derivative is $0$. For $S>K$, $C(S)=S-K$ so the derivative is $1$. At $S=K$ the one-sided derivatives differ, so expiry delta is undefined at the kink.

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.