Static Hedging and Pricing American Knock-Out Options

This article extends the static hedge portfolio (SHP) approach of Derman et al. [1995] and Carr et al. [1998] to price and/or hedge American knock-out options. We construct a SHP to match the complicated boundary conditions of American barrier options. Detailed analyses of the profit and loss distributions suggest that the hedging effectiveness of a bimonthly SHP is far less risky than that of a delta-hedging portfolio with daily rebalance. Moreover, numerical results indicate that the efficiency of the proposed method is comparable to Boyle and Tian [1999] for pricing American knock-out options under the constant elasticity of variance (CEV) model of Cox [1975]. In particular, the recalculation of the option prices and hedge ratios under the proposed method is much easier and quicker than the tree methods.