Backward option pricing
= Backward option pricing
At each node of a binomial tree, a claim with next-period values $V_u,V_d$ has value
$$
V=\frac{qV_u+(1-q)V_d}{1+r},
$$
where $q$ is the local <risk-neutral probability in a binomial market>. For an American claim, replace this continuation value by the maximum of continuation and immediate exercise value.