Exotic Options

Abstract

In the preceding chapters, we have focused on the two standard classes of options — that is, call and put options of European and American style. The aim of this chapter is to study examples of more sophisticated option contracts. For convenience, we give the generic name exotic option to any option contract which is not a standard European or American option. Although the payoffs of exotic options are given by similar expressions for both spot and futures options, it is clear that the corresponding valuation formulas would not agree. Therefore, it should be made clear that we will restrict our attention to the case of exotic spot options. We find it convenient to classify the large family of exotic options as follows (cf. Rubinstein (1991b)):

• (a) packages — options that are equivalent to a portfolio of standard European options, cash and the underlying asset (stock, say);

• (b) forward-start options — options that are paid for in the present but received by holders at a prespecified future date;

• (c) chooser options — option contracts that are chosen by their holders to be call or put at a prescribed future date;

• (d) compound options — option contracts with other options playing the role of the underlying assets;

• (e) binary options — contracts whose payoff is defined by means of some binary function;

• (f) barrier options — options whose payoff depends on whether the underlying asset price reaches some barrier during the option’s lifetime;

• (g) lookback options — options whose payoff depends, in particular, on the minimum or maximum price of the underlying asset during options’ lifetimes;

• (h) Asian options — options whose payoff depends on the average price of the underlying asset during a prespecified period;

• (i) basket options — options with a payoff depending on the average of prices of several assets;

• (j) α-quantile options — options whose payoff depends on the percentage of time that the price of the underlying asset remains below some level;

• (k) combined options on several assets — these include, for instance, options on the minimum or maximum price of two risky assets;

• (l) Russian option — a “user friendly” variant of a standard American option.