Hi, sorry if the question is trivial/specific. I am trying to follow the derivation in the paperLink for the paperwhere the objective is to inductively find the (2n+1) unknowns (n risk-neutral probabilities and n+1 price nodes) given information up to the n-th layer. I am lost at EQ.4 (PDF page 12), because1. Only lambda_1, ..., lambda_n are known but EQ.4 seems to require (n+1) lambda's (see the summation index); and2. If we group the terms in this way, the very bottom and the very top nodes in the new layer would be "orphaned", i.e. the top node in the new layer should only be accessible from below but the sum in EQ.4 demands that it is also accessible from above.Am I missing or overlooking something? Thanks.

Not sure about the exact paper, but the usual logic with top and bottom nodes in finite difference trees is to understand the boundary condition, i.e. does d_price / d_layer become constant at the top and bottom, and we make sure we take a tree with boundaries sufficiently far out to ensure this?If so then top node = 2nd node + (2nd node - 3rd node)etc

Try www.Volopta.com I think the code is available there.