American Step Options

This paper examines the valuation of American knock-out and knock-in step options. The structures of the immediate exercise regions of the various contracts are identified. Typical properties of American vanilla calls, such as... [ view full abstract ]

This paper examines the valuation of American knock-out and knock-in step options. The structures of the immediate exercise regions of the various contracts are identified. Typical properties of American vanilla calls, such as up-connectedness of the exercise region, convexity of its t-section or uniqueness of the optimal exercise boundary, are shown to fail in some cases. Early exercise premium representations of step option prices, involving the Laplace transforms of the joint laws of Brownian motion and its occupation times, are derived. Systems of coupled integral equations for the components of the exercise boundary are deduced.