In most ROA calculations, the volatility of the project payoff is assumed to be relatively constant over the option life and is represented by a single aggregate factor. Therefore, a single volatility factor is used across the binomial tree to represent the option life. However, if the volatility is expected to change during the option life and is significant, it can be accounted for by modifying the binomial method. Start with the initial volatility factor, build the binomial tree, and calculate the asset values at each node of the tree using the corresponding up and down factors up to the point where the volatility changes. From that point on, calculate the asset values using the new up and down factors related to the new volatility factor, which will result in a nonrecombining lattice. The option value calculation method using backward induction will be the same for the entire tree. The following example for an option to wait demonstrates the calculations involved. (Although this is a simple option by definition, it requires an advanced form of the lattice method using the nonrecombining lattice and hence its inclusion in this chapter on advanced options.)

1. Frame the application

EnviroTechno, an environmental technology company, is considering an investment in a new patented product that can help industries comply with an environmental regulation that is under consideration by the U.S. Congress. Whereas the regulation is expected to be passed two years from now, many multinational companies based in the United...