The pricing of dual-expiry exotics

Abstract

This paper develops a new technique for pricing a class of exotic options that are characterized by two expiry dates. Examples of such exotics include compound options, chooser options, extendable options, shout options, partial barrier options and others. The method, based on the partial differential equation approach to option pricing, however requires no formal solution of such equations. Instead, the method exploits the observation that dual expiry options have payoffs that can be perfectly replicated by a particular set of first and second order binary options. Hence, in order to avoid arbitrage, the exotic option prices are obtained by static replication with respect to this family of binaries. The representation of prices in terms of these binaries is also quite general and does not depend on any particular underlying asset price dynamics. Closed form expressions agreeing with published results are given for the case of log-normal asset price dynamics and standard Black-Scholes assumptions.