Extensions of MPO to Exotic Options

Abstract

Exotic options are 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, quanto options, exchange 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 options. Normally, exotic options are traded in OTC markets. Recently, this situation has somehow changed. The American Stock Exchange trades quanto options while the New York Mercantile Exchange provides spread options. With financial risks being understood better, exotic options are more and more widely employed by financial institutions, big corporations and fund managers. Some exotic options have already become commonplace in risk management due to their case-orientated properties. According to whether they possess an exotic payoff or probability structure, exotic options are valued in a different manner. Generally speaking, options with a complicated probability are path-dependent and therefore difficult to price. However, in the Black-Scholes world, closed-form pricing formulae for almost all exotic options have been derived.52 KeywordsInterest RateStochastic VolatilityCall OptionExchange OptionStrike PriceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.