"simple" discretized expression for the drift then allows for forward rates to be expressed in a binomial lattice. For these forward rate-based models, dependent on volatility assumptions, the lattice might not recombine. (This means that an "up-move" followed by a "down-move" will not give the same result as a "down-move" followed by an "up-move".) In this case, the Lattice is sometimes referred to as a "bush", and the number of nodes grows exponentially as a function of number of time-steps. A recombining binomial tree methodology is also available for the Libor Market Model. As regards the short-rate models, these are, in turn, further categorized: these will be either equilibrium-based (Vasicek and CIR) or arbitrage-free (Ho–Lee and subsequent). This distinction: for equilibrium-based models the yield curve is an output from the model, while for arbitrage-free models the yield curve is an input to the model. In the former case, the approach is to "calibrate" the model parameters, such that bond prices produced by the model, in its continuous form, best fit observed market prices. The tree is then built as a function of these parameters. In the latter case, the calibration is directly on the lattice: the fit is to both the current term structure of interest rates (i.e. the yield curve), and the corresponding volatility structure. Here, calibration means that the interest-rate-tree reproduces the prices of the zero-coupon bonds—and any other interest-rate sensitive securities—used in constructing the yield curve; note the parallel to the implied trees for equity above, and compare Bootstrapping (finance). For models assuming a normal distribution (such as Ho-Lee), calibration may be performed analytically, while for log-normal models the calibration is via a root-finding algorithm; see for example, the boxed-description under Black–Derman–Toy model. The volatility structure—i.e. vertical node-spacing—here reflects the volatility of rates during the quarter, or other period, corresponding to the lattice time-step. (Some analysts use "realized volatility", i.e. of the rates applicable historically for the time-step; to be market-consistent, analysts generally prefer to use current interest rate cap prices, and the implied volatility for the Black-76-prices of each component caplet; see .) Given this functional link to volatility, note now the resultant difference in the construction relative to equity implied trees: for interest rates, the volatility is known for each time-step, and the node-values (i.e. interest rates) must be solved for specified risk neutral probabilities; for equity, on the other hand, a single volatility cannot