Summary

Most of the concrete examples of options considered so far have been the standard examples of calls and puts. Such options have liquid markets, their prices are fairly well determined and margins are competitive. Any option that is not one of these vanilla calls or puts is called an exotic option. Such options are introduced to extend a bank's product range or to meet hedging and speculative needs of clients. There are usually no markets in these options and they are bought and sold purely ‘over the counter’. Although the principles of pricing and hedging exotics are exactly the same as for vanillas, risk management requires care. Not only are these exotic products much less liquid than standard options, but they often have discontinuous payoffs and so can have huge ‘deltas’ close to the expiry time making them difficult to hedge.

This chapter is devoted to examples of exotic options. The simplest exotics to price and hedge are packages, that is, options for which the payoff is a combination of our standard ‘vanilla’ options and the underlying asset. We already encountered such options in §1.1. We relegate their valuation to the exercises. The next simplest examples are European options, meaning options whose payoff is a function of the stock price at the maturity time. The payoffs considered in §6.1 are discontinuous and we discover potential hedging problems. In §6.2 we turn our attention to multistage options.