THE PRICING AND HEDGING OF LIMITED EXERCISE CAPS AND SPREADS

Capped options are barrier option spreads that automatically create simultaneous long and short positions. Exchange‐traded capped options were introduced in 1991, though with limited volume. Such options, however, have traded on the over‐the‐counter markets for several years. Most of these options have the unusual feature that they automatically exercise when the underlying asset closes beyond a critical strike, making them a hybrid of European and American options. In this paper I present their boundary conditions and examine the prices, deltas, gammas, and thetas of caps as well as spreads constructed with European and American options. I also examine the effect of permitting exercise based only on the closing price as opposed to exercise at any time the critical strike is reached. I show that assuming that exercise can occur at any time can lead to serious pricing errors. The results have implications for the pricing of barrier options in general, which nearly always exercise early based only on the closing price.