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

Journal of Financial and Quantitative Analysis 2005 40(3), 671-691
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.

Analysis of the Warrant Hedge in a Stable Paretian Market

Journal of Financial and Quantitative Analysis 1977 12(1), 85
A stock purchase warrant gives the owner the option to buy some predetermined number of shares of the associated common stock at a specified price over a stipulated time period. The specified price is called the exercise price of the warrant. The stipulated time period is quite variable, though the life of a typical warrant will exceed five years.