Pricing Path Dependent Exotic Options: a Comprehensive Mathematical Framework

This book presents a novel two-part framework for pricing all conceivable barrier and lookback options in the Black-Scholes world. The first part calls for the static replication of vanilla and exotic option prices into simpler European derivative contracts, termed binary options. These are of various orders and types, and are expressible in terms of the multi-normal distribution function. The second part values all types of weakly path-dependent options via the properties of the Image Method of Buchen, and the various extensions developed here. With our methods, the task of pricing any option with either barrier features (whether single, double or exotic), or lookback features, or both, is reducible to pricing equivalent portfolios of the path-independent binaries we have defined. All pricing presented using the framework is accomplished without recourse to formally solving PDEs nor calculating expectations. We use our methods to price all the standard and exotic barrier and lookback options extant in the literature, as well as to create and price numerous non-trivial extensions in both the single and multi-dimensional case.