The key difference between American and European options relates to when the options can be exercised:
- A may be exercised only at the ''expiry date'' of the option, i.e. at a single pre-defined point in time.
- An on the other hand may be exercised at any time before the expiry date.
For both, the pay-off - when it occurs - is via:
: Max (S – K), 0 , for a Call Option
:Max (K – S), 0 , for a Put Option :
(Where K is the Strike Price and S is the spot price of the underlying asset)
Option contracts traded on Futures Exchange s are mainly American-style, whereas those traded Over-the-counter are mainly European.
European options are typically valued using the Black-Scholes or Black Model formula. This is a simple equation with a closed-form solution that has become standard in the financial community. There are no general formulae for American options, but a choice of models to approximate the price are available (for example Whaley , Binomial Options Model , Monte Carlo and others - there is no consensus on which is preferable).
American options are rarely exercised early. This is because any option has a non-negative Time Value and is usually worth more unexercised. Owners who wish to realise the full value of their option will mostly prefer to sell it on, rather than exercised immediately, sacrificing the time value.
Where an American and a European option are otherwise identical (having the same Strike Price , etc.), the American option will be worth at least as much as the European (which it entails). If it is worth more, then the difference is a guide to the likelihood of early exercise. In practice, one can calculate the Black-Scholes price of a European option that is equivalent to the American option (except for the exercise dates of course). The difference between the two prices can then be used to Calibrate the more complex American option model.
To account for the American's higher value there must be some situations in which it is optimal to exercise the American option before the expiration date. This can arise in several ways, such as:
- A deep ITM Currency option (FX option) where the strike currency has a lower interest rate than the currency to be received will often be exercised early because the time value sacrificed is less valuable than the expected depreciation of the received currency against the strike.
- A Put Option on Gold will be exercised early when deep ITM, because gold tends to hold its value where as the Currency used as the strike is often expected to lose value through Inflation if the holder waits until final maturity to exercise the option (they will almost certainly exercise a contract deep ITM, minimizing its time value).
There are other, more unusual exercise styles in which the pay-off value remains the same as a standard option (as in the classic American and European options above) but where early exercise occurs differently:
- A is an option where the buyer has the right to exercise at a set (always discretely spaced) number of times. For example a typical Bermudan Swaption might confer the opportunity to enter into an Interest Rate Swap . The option holder might decide to enter into the swap at the first exercise date (and so enter into, say, a ten-year swap) or defer and have the opportunity to enter in six months time (and so enter a nine-year and six-month swap). Most exotic interest rate options are of Bermudian style.
- A is not an Interest Rate Cap but a conventional option with a pre-defined profit cap written into the contract. A capped-style option is ''automatically exercised'' when the underlying security closes at a price making the option's Mark To Market match the specified amount.
- A is an option on another option, and as such presents the holder with two separate exercise dates and decisions. If the first exercise date arrives and the 'inner' option's market price is below the agreed strike the first option will be exercised (European style), giving the holder a further option at final maturity.
- A allows the holder effectively two exercise dates: during the life of the option they can (at any time) "shout" to the seller that they are locking-in the current price, and if this gives them a better deal than the pay-off at maturity they'll use the underlying price on the shout date rather than the price at maturity to calculate their final pay-off.
- A gives the purchaser the right to exercise one and only one call or put on any one of a number of specified exercise dates. Penalites are imposed on the buyer if the net volume purchased exceeds or falls below specified upper and lower limits. Allows the buyer to "swing" the price of the underlying asset. Primarily used in energy trading.
These options can be exercised either European style or American style; they differ from the plain Vanilla Option only in the calculation of their pay-off value:
- A (or '''composite option''') is an option on some underlying in one Currency with a strike denominated in another currency. For example a standard Call Option on IBM, which is denominated in Dollars pays (S-K,0) (where S is the stock price at maturity and K is the strike). A composite stock option might pay £MAX(S-K,0). The pricing of such options naturally needs to take into account the Correlation between the Exchange Rate of the two currencies involved and the underlying stock price. The value of a cross option will be higher than a similar Vanilla Option since the Volatility of the strike against the underlying asset contains both the asset's volatility and the Exchange Rate 's.
- A is a cross option in which the exchange rate is fixed at the outset of the trade. This is less valuable than a cross option and has a similar value to a vanilla. (The jargon sometimes includes cross options as a type of quanto).
- An is the confusingly-named right to exchange one asset for another (such as a sugar future for a corporate Bond ). Such options are not traded on futures exchanges. Similarly '''rainbow options''' and '''basket options''' are options on a package of several underlyings.
The following " Exotic Option s" are still options, but have payoffs calculated quite differently from those above. Although these instruments are far more unusual they can also vary in exercise style (at least theoretically) between European and American:
- A is a Path Dependent option where the option owner has the right to buy (respectively sell) the underlying instrument at its lowest (respectively highest) price over some preceding period.
- An is an option where the payoff is not determined by the underlying price at maturity but by the average underlying price over some pre-set period of time. For example an asian call option might pay MAX(DAILY_AVERAGE_OVER_LAST_THREE_MONTHS(S) - K, 0).
- A is a lookback option which runs for perpetuity. That is, there is no end to the period into which the owner can look back.
- A or '''Israeli option''' is an option where the writer has the opportunity to cancel the option he has offered, but must pay the payoff at that point plus a penalty fee.
- The payoff of a is dependent of the amount of time the option has spent above or below a strike price.
- A involves a mechanism where if a price is crossed by the underlying, the option either can be exercised or can no longer be exercised.
- A (also known as a digital option) pays a fixed amount, or nothing at all, depending on the price of the underlying instrument at maturity.
- A gives the purchaser a fixed period of time to decide whether the derivative will be a vanilla call or put.
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