# 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....

-

## 1 Answer

R denotes the implied risk-neutral cumulative growth which is different for each note.

You get them through: 1 + cumulative risk-neutral return through the tree to a particular node.

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

-
@ Freddy thanks for your answer, but "1+ cumulative risk-neutral return", what is that? Could you please do an example calculation in my case? So I am just reconstructing the paper, would be nice if you can show me this using this one. – user1690846 Jan 6 '13 at 9:40
you asking this question I respectfully recommend you to start over and first familiarize yourself with the basic building blocks before you hack away functions on spreadsheets. Conversely, programmers never start hitting code into their machines but rather carefully design use cases, requirements, available resources... Maybe you want to focus on a more basic paper which touches on the basics of the binomial tree model. – Matt Wolf Jan 6 '13 at 12:26