Derivatives

CHAPTER 31Exotic Options

Aims

• To analyse various types of exotic option whose payoffs are path dependent.
• To use the BOPM and MCS to price various exotic (path dependent) options.
• To demonstrate the use of Asian (or average rate) options, barrier options and other exotics such as lookback, forward start and chooser options.

In this chapter we explain how some of the more exotic options contracts (e.g. on stocks, FX, and commodities) can be used in speculation and hedging. Closed-form solutions for the price of exotic options are often not possible and we demonstrate how some of these options are priced using binomial trees and Monte Carlo simulation (MCS).

It is difficult to say where plain vanilla options end and exotics begin. Generally speaking, the payoffs from exotics are more complex than those from vanilla options. As a result, exotics are largely OTC instruments and their payoffs may sometimes be ‘structured’ to an individual client's needs – hence the term structured finance is sometimes used to denote options with complex payoffs.

The payoff to a European option depends only on the price of the underlying at maturity, (since it can only be exercised at maturity) and does not depend on the path taken to reach . European options are said to be path independent. On the ...