Work out what a floating-rate bond with a cap or a floor is worth

A capped floater pays the reference rate, set at the start of each period and paid at the end, but never more than the cap. On a tree, value it backward: at each node the coupon paid next period is the lower of the node rate and the cap, and value = [½ × (value up + value down) + coupon] ÷ (1 + node rate). Without the cap the floater is worth par. The cap's value, held by the issuer, is par minus the capped floater's value. A floored floater uses the higher of the rate and the floor, and the floor's value is the excess over par. Apply the cap or floor at every node, including today's rate.