I'm currently looking into calculating the "option to switch use" to determine the benefit of the ability to switch between two technologies at any point in time (american option). This is also called an "exchange option" for financial options.
Trigeorgis calculates the value of flexibility in his book (p173) as: $F(A \rightarrow B) = S_0(A \rightarrow B) + S_1(A \rightarrow B) + S_2(A \rightarrow B)$
where $S_t$ is the value of the option at each point in time when switching from technology A to technology B. The value of the option is therefore calculated as the sum(!) of the options values from each point in time backwards to $t=0$.
Unfortunately there is no explanation there why this is treated different than any other calculation of a binomial lattice I found. In any other case I found there is just one backwards pass calculated to find the value at the root node. This final value is then treated as the value of the option.
Edit: Question: Why is Trigeorgis calculating the option value differently than everyone else?
Any insights would be greatly appreciated!