Use a two-period binomial model to work out no-arbitrage values for American and European options
The idea
In a two-period tree, find the terminal prices S u², S u d and S d², their payoffs, and roll back a step at a time with π, discounting each step at the one-period rate. A European option needs only the terminal payoffs. An American option adds a check at each earlier node: its value there is the larger of the rolled-back value and the value of exercising now. Early exercise can pay for a deep in-the-money American put, because receiving the strike early earns interest; an American call on a non-dividend-paying share is never exercised early and equals the European call. The trap is valuing an American put from terminal payoffs alone, which gives the European value.
In the app: 2 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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