I have a trinomial tree and want to price barrier options using it.For down and out option all nodes which lie below the barrier are set to zero which is easy.However what should I zero (or otherwise change) in order to calculate the same for down and in options?NB. up and down probabilities vary throughout the tree as it is an implied treeTHANKS

Just code the vanillas (no barrier).Then use:Down-and-out + Down-and-in = Vanillaregards,

I've done it that way, but, if possible, I'd like to be able to do it itself as well.

ok, if you really want to ...At the down-and-in barrier, the value is a vanillawith underling price = barrier price and time-to-go = time-to-go at that node.So use that for your boundary condition.regards,

QuoteOriginally posted by: BasketOptionsI've done it that way, but, if possible, I'd like to be able to do it itself as well.Closely related to trinomial method is explicit finite difference method that is very easy to program. Barriers will be just boundary conditions.Continuous monitoring or discrete?

Sorry I don't quite see what your saying.All nodes below the barrier are the vanilla values.There are also nodes which clearly could never have broken the barrierHowever how should I deal with other nodes whose route to there may or may note have brached the barrier.Many thanks,

I think I see your problem -- you have createda trinomial tree which includes many nodes below thebarrier. In your down-and-out iteration you iterated over allthose nodes. Here is my suggestion.1. Put the barrier exactly on a node if it's not already. 2. Fill in the values on those particular barrier nodes with the vanilla formula I gave.3. Use backwards trinomial iterationV_new(i) = p1 V_old(i-1) + p2 V_old(i) + p3 V_old(i+1)where i on the left-hand-side ranges *only* over nodes above the barrier.Then, at most you will need a value of V_old on the right-hand-side exactly on the barrier,and you will have already filled in those values at step 2. You will never need anyother values for nodes below the barrier. Hope it helps,alan p.s. Thinking about it a little more, I don't see any problem witha backwards iteration over *all* the nodes from expiration, even if many of themare below the barrier.

With FDM the barrier nodes and the lattice nodes coincide, so that's one problem less., 2 cents

try adaptive mesh method which is quite effective in dealing with barrier option pricing using trinomial trees

this is my guess:down-and-in barrier options are valid only when the barrier is crossed. so you should first price all the nodes along the barrier with your tree payoffs and probabilities. then modify the tree by: 1. keeping the calculated payoffs along the barrier; 2. setting all nodes above the barrier to zero payoff; 3. ignore the nodes strictly below the barrier. you can now redo the iteration for all the nodes strictly above the barrier. However both binomial and trinomial tree methods converge slowly to the true value for barrier options since the discretized node values don't always coincide with the exact barrier level . Refer to Derman, Kani et all (1995) on improving tree methods for barrier options.