Peter, a warrant and an option are the same thing in term of pricing... a warrant is just a kind of packaged option (one warant =100 single option fopr example...) to simplify the price (you would pay $2 instead of $0.02).
Otherwise, an in the money (ITM) call option on a stock is often exercised just before the stock pays a dividend which would lower its value by more than the option's remaining time value... so the pricing of this instrument is path dependant... it will be at each node is Max[Binomial Value, Exercise Value]. These 2 values are the same for a european option or if you use only a dividend yield instead of a discrete dividend timeschedule.

Hope it helps...