Bounds for a Call

Bounds for a Put

American Call: Non-dividend paying stock

Early exercise for Non-dividend Stock

Early Exercise for Discrete Dividend Stock

Early exercise on American Put

Call order
(K1< K2< K3)

Difference in calls
(No arbitrage)

No arbitrage, calls

Put order
(K1<K2<K3)

Difference in Puts
(No arbitrage)

No arbitrage, Puts
(K1 < K2 < K3)