We develop a straightforward procedure to price derivatives by a bivariate tree when the underlying process is a jump-diffusion. Probabilities and jump sizes are derived are derived by matching higher order moments or cumulants. We give comparisons with other published results along with convergence proofs and estimates of the order of convergence. The bivariate tree approach is particularly useful for pricing long-term American options and long-term real options because of its robustness and flexibility. We illustrate the pedagogy in an application involving a long-term investment project.

For firms that adopted economic profit plans between 1983 and 1996, we document changes in investment behavior that lead to improvements in operating performance and growth opportunities relative to these firms' past performance. The improvements, however, are similar to those realized by a set of non-adopting control firms that are selected on the basis of a logistic regression model of adoption choice. We then consider the possibility that some firms are better candidates for economic profit plans than others and classify adopters according to whether they make anticipated or surprising choices based on the adoption choice model. We find that anticipated adopters make changes in investment behavior that reduce invested capital and allow them to become more profitable than a sample of control firms that were expected to adopt but chose to continue using a traditional plan. A similar analysis of surprise adopters does not reveal significant performance differences relative to a sample of anticipated non-adopters. The classification analysis suggests that economic profit plans work best for firms that are expected to adopt such plans based on pre-adoption operating, organizational, financial, and compensation characteristics.

Lockups are agreements made by insiders of stock-issuing firms to abstain from selling shares for a specified period of time after the issue. Brav and Gompers (2003) suggest that lockups are a bonding solution to a moral hazard problem and not a signaling solution to an adverse selection problem. We challenge this conclusion theoretically and empirically. In our model, insiders of good firms signal by putting and keeping (locking up) their money where their mouths are. Our model yields two comparative statics: lockups should be shorter when a firm is i) more transparent and/or ii) more risky. Using a sample of 4,013 initial public offerings and 3,279 seasoned equity offerings between 1988 and 1999, we find empirical support for our theoretical predictions.