Static Hedging and Pricing American Knock-Out Options

Abstract

Delta hedging is the time-honored approach to option risk management, but it requires frequent rebalancing to keep the risk exposure hedged and bear the associated transactions costs. An alternative approach is to set up a static hedge portfolio, consisting of some number of options at the outset, that is designed to cover the contingent payoffs of the option being hedged without extensive rebalancing. In this article, the authors apply the static hedge concept to American barrier options and show how to set up the static portfolios, which is the only time-consuming part of the problem. Unlike delta hedging, which requires essentially the same problem to be solved repeatedly in rebalancing the hedge, once the static portfolio is set up, subsequent calculations to update the option prices are very fast. Moreover, the hedging performance in terms of tracking error is distinctly superior in static hedging when compared to delta hedging and is only slightly affected by the need to use options with standardized strikes.