Time-dependent barrier option values

Abstract

INTRODUCTION European barrier options are path-dependent options in which the existence of the European options depends on whether the underlying asset price has touched a barrier level during the option life. They have emerged as significant products for hedging and investment in foreign exchange, equity, and commodity markets since the late 1980s, largely in the overthe -counter (OTC) markets. The only barrier option that is traded on the options exchanges is the capped index spread on the S&P 100 and S&P 500. The cap is automatically exercised with a fixed profit when the underlying price closes beyond the barrier level. Thus the option is canceled with a fixed return at the barrier level. Its pricing and hedging are discussed by Chance (1994). An example of a barrier option is an up-and-out put. An investor could buy an up-and-out U.S. dollar put (Japanese yen call) instead of an ordinary U.S. dollar put to hedge the value of U.S. dollar versus Japanese yen. The put optio

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