Cox--Ross--Rubinstein model
= Cox--Ross--Rubinstein model
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In the Cox--Ross--Rubinstein model, a stock changes at each discrete time by an up factor $U$ or a down factor $D$, while the money-market account changes by a deterministic factor $R$. After discounting by the money-market account, the factors are $u=U/R$ and $d=D/R$. The model is arbitrage-free exactly when $D<R<U$, equivalently $d<1<u$.