When it is important to incorporate the volatility smile, or surface, implied trees can be constructed. Here, the tree is solved such that it successfully reproduces selected (all) market prices, across various strikes and expirations. These trees thus "ensure that all European standard options (with strikes and maturities coinciding with the tree nodes) will have theoretical values which match their market prices". Using the calibrated lattice one can then price options with strike / maturity combinations not quoted in the market, such that these prices are consistent with observed volatility patterns. There exist both implied binomial trees, often Rubinstein IBTs (R-IBT), and implied trinomial trees, often Derman-Kani-Chriss (DKC; superseding the DK-IBT). The former is easier built, but is consistent with one maturity only; the latter will be consistent with, but at the same time requires, known (or interpolated) prices at all time-steps and nodes. (DKC is effectively a discretized local volatility model.)