Static Hedging and Pricing American Options Under General Processes

Abstract

This paper utilizes the static portfolio approach of Derman, Ergener, and Kani (1995) and Carr, Ellis, and Gupta (1998) to hedging and pricing American options under many general processes beyond the Black-Scholes model. The static hedging portfolio (SHP) of an American option is formulated by applying the value-matching and smooth-pasting conditions at the early exercise boundaries. The numerical results indicate that our static hedging approach for pricing American options are accurate across different models, including the Black-Scholes model, the CEV model of Cox (1975), and the jump-diffusion model of Merton (1976). Our static hedging approach also provides simple and intuitive derivations of the early exercise boundaries near expiration.