The barrier option adds a barrier value (for example, H = $95.00) and it the option can either "knock-out" (ie, get knocked-out if the barrier is breached) or "knock-in" (ie, come into existence if the barrier is breached. If the barrier is below the asset price, it is either a down-and-out or down-and-in barrier option; if the barrier is above the asset price, it is either an up-and-out or up-and-in barrier option. The key valuation relationship is c(ui) + c(uo) = c and c(di) + c(do) = c.
David's XLS: https://trtl.bz/2P1BiNr
David's XLS: https://trtl.bz/2P1BiNr
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