Could you help me build an option value formula from the binomial option pricing model(with discrete probability factors). The problem is that I am trying to find out the value function of R&D project where individual development research(performance, reliability, yield, etc) must be all accomplished. I made the sample Binomial tree below to explain the problem situation. I divided research into 2 types: performance research and other research in order to make the situation simpler. I think option price can be solved by backwarding. You can modify the binomial tree or the problem if needed.

Idea: when developing new products, R&D process should be done before manufacturing. Often R&D projects are consist of multiple development research. So, my goal is to make the value formula of R&D project( or value or contribution rate formula of individual research if possible) using real option method.

( I_f = manufacturing cost)

New proudct development Project success probability of performance research: P P 4: success probability of : Pot Pot other researches (total) Performance other Success (0) O O X Q Fail(x) X CF up X =CF X U performance other wwwwwwww CFdw O O = CF x D O X X O X X P give up proceed -Cp-Cot Decision node Chance node End node manufacture (F) give up give up proceed VF (CFU) - IF 0 0 CFup =CF x U CFw = CFxUX D performance Q X performance Q X performace other wwwwwww 9 0 9 X give up X 0 CF =CF x U Xx X performance proceed other wwwwwww CF O O -Cp-Cot = CFxUxD O X X Q X X VF (CFU) - IF manufacture (F) 0 give up Due (max N tries=N-year research) New proudct development Project success probability of performance research: P P 4: success probability of : Pot Pot other researches (total) Performance other Success (0) O O X Q Fail(x) X CF up X =CF X U performance other wwwwwwww CFdw O O = CF x D O X X O X X P give up proceed -Cp-Cot Decision node Chance node End node manufacture (F) give up give up proceed VF (CFU) - IF 0 0 CFup =CF x U CFw = CFxUX D performance Q X performance Q X performace other wwwwwww 9 0 9 X give up X 0 CF =CF x U Xx X performance proceed other wwwwwww CF O O -Cp-Cot = CFxUxD O X X Q X X VF (CFU) - IF manufacture (F) 0 give up Due (max N tries=N-year research)