Exotic Options with Stochastic Volatilities

Abstract

Exotic option is a common name for a number of options either with an unconventional payoff structure or with a complicated probability structure (i.e., path-dependent options). There is a long list of financial derivatives belonging to this class: barrier options, Asian options, correlation options, spread options, exchange options, clique options etc. Most of them are generated in the course of the expansion of the financial derivative business since the 1970s, and are referred to as second generation options although some exotic options, for example, barrier options, are as old as standard European-style options, and are traded in over-the-counter (OTC) markets. Recently, this situation has somehow changed. The American Stock Exchange trades quanto options while the New York Mercantile Exchange provides spread options.