Pricing European and American Derivatives under a Jump-Diffusion Process: A Bivariate Tree Approach

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.