Note that there is no discounting here the interest rate appears only as part of the construction. This approach is therefore used in preference to others where it is not clear whether the risk free rate may be applied as the discount rate at each decision point, or whether, instead, a premium over risk free, differing by state, would be required. The best example of this would be under real options analysis where managements' actions actually change the risk characteristics of the project in question, and hence the Required rate of return could differ in the up- and down-states. Here, in the above formulae, we then have: "Δ × "S up" - B × (1 + r up)..." and "Δ × "S down" - B × (1 + r down)...". See Real options valuation#Technical considerations. (Another case where the modelling assumptions may depart from rational pricing is the valuation of employee stock options.)