An American option adds the right to exercise before expiry.
highlighted = computed this step
Exercise timing
An American put can be exercised any time up to expiry. A European option waits until expiry. Here the strike is $105.00 on a two-step tree that starts at $100.00, moves up by 6/5 or down by 9/10, and uses a 5% risk-free rate.
K=$105.00,S0=$100.00,r=5%
Tree values
The diagram shows the recomputed American put values. The diagram highlights the node where immediate exercise beats holding.
American value is recomputed at each node
Model note
This is a binomial model with constant up and down factors, one stated rate, frictionless trading, no transaction costs, fees, taxes, credit risk, liquidity limits, or default. The American put value is a model value under those stated assumptions, not a market price. This is descriptive, not investment advice.