# Rubinsteins Implied Binomial Tree - how to calculate the cumulative returns

I am working on Rubinsteins IBT and use the following paper to implement this into excel:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=541744

the original paper can be found here:

http://www.haas.berkeley.edu/groups/finance/WP/rpf232.pdf

I am stuck in the last step: I calculated the path probabilities, denoted by "Q". In the paper "Implied Binomial Trees in Excel without VBA" page 7 and 17.

So I have now the results of Panel B on page 17. These are the Q at the last node, now I calculate the Q at the nodes before with $Q=Q^+ + Q^-$. So I have the resulting path probabilities Q shown in the uploaded and attached picture (the numbers are a bit different from the paper, because my excel solver was not that accurate, but the numbers should be the same). So now I want to calculate the "R". These are the cumulative returns. In the paper it says on page 7: $R=(qR^+ + (1-q)R^-)/r$.

I know that the small qs are the up probabilities, calculated by $q=Q^+/Q$. Ok, the small r is a discounting factor, ok. But what are the $R^+$ and $R^-$. Where do I get them? Are these just the original prices form the CRR binomial tree?

Thanks a lot!

(in the excel file which can be downloaded, this step is not implemented)

edit:

It should be in the paper, though, for example "a 20% growth in the underlying gives R = 1.20"

My underlying, values u and d calculated by CRR? So the values of the underlying are: @ Freddy Could you please use my example and do an example calculation? The comment is to general and not specific enough....