## Exotic Options

Numerous variations on the basic design of options have been proposed, Each variation offers effective control of the risk perceived by a certain group of investors or eases execution and bookkeeping. We list a few of these variations here:

1. Bermudan option In this option, the allowable exercise dates are restricted, in some case to specific dates and in other cases to specific periods within the lifetime of the option. Warrants on stock often have this characteristic.

2. Forward start options These are options that are paid for at one date, but do not begin until a later date.

3. Compound options A compound option is an option on an option,

4. "As you like it" or "chooser" options The holder of an "as you like it" option can, after a specified time, declare the option to be either a put or a call

5. CAPs These options restrict the amount of profit that can be made by the option holder by automatically exercising once the profit reaches a specified level. A $20 CAP on a call option, means that once the stock price rises to $20 over the strike price, the option is exercised,

6. LEAFS This term stands for "Long-term Equity Anticipation Securities." They are long-term, exchange-traded options with exercise dates as far as .3 years into the future.

7. Digital options In a digital option the payoff is $1 if the option is in the money and zero otherwise A European digital call option, for example, has payoff I if S(T) > K, and 0 if 5(7) < K, where K is the strike price.

8. Exchange options Such an option gives one the right to exchange one specified security for another.

9„ Yield-based options A yield-based option on a bond defines the exercise value in terms of yield rather than price. Hence the holder of a yield-based call option benefits if bond prices decrease since yields move in the opposite direction to prices,

10- Cross-ratio options These are foreign-currency options denominated in another foreign currency; for example, a call on German marks with an exercise price in Japanese yen.

11. Knockout options These options terminate (with zero value) once the price of the underlying asset reaches a specified point. For calls these are "down and out" options, which terminate once the price of the underlying asset falls below a specified level. For puts the analogous option is a "up and out" option,

12. Discontinuous options These options have payoffs that are discontinuous functions of the price of the underlying asset, For example, a call option may pay either zero or $20, depending on whether the final price of the underlying asset is below or above a specified strike price.

13. Lookback options In a lookback option the effective strike price is not specified, but is determined by the minimum (in the case of a call) or maximum (in the case of a put) of the price of the underlying asset during the period of the option For example, a European-style lookback call option has a payoff equal to max (¿V — ,Smin, 0) = S'i — Sn1i„, where is the minimum value of the price S over the period from initiation to the termination time T Such options are very attractive to investors, since in fact they always have positive value (unless 5y = £,„jn) Of course their prices reflect the apparent attractiveness

14. Asian options The payoff of Asian options depends on the average price 5aVg of the underlying asset during the period of the option There are basically two ways that the average can be used. In one, Savg serves as the strike price, so that the payoff of a corresponding call, for example, is max (Sj — Savg, 0), In the second type, Snvg is substituted for the final price Thus the payoff of the corresponding call is max(S;,vg — /CO), where K is a specified strike price.

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