Option style

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(Redirected from American option)

The style or family of a financial option is a general term denoting the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of option contracts are either european or american style options:

  • A european option may be exercised only at the maturity of the option, i.e. at a single pre-defined point in time.
  • An american option on the other hand may be exercised at any time before expiry.
Contents

Difference in Value Between American and European Options

Oddly, american options are rarely exercised early. That is because any option has a time value and is usually worth more unexercised. Buyers who wish to realise the full value of their option will mostly prefer to sell it on (rather than exercise immediately, sacrificing the time value). Many stock exchanges deal primarily in American-style option contracts, and sales of such options on high volume underlyings (such as the S&P Index) can now be swiftly executed through a liquid, & public, listed market. For American options on more obscure equities or in markets primarily using Europeans an over the counter (OTC) private sale will be necessary (usually at a higher spread). In general, the European style is the more common and therefore the market in these trades tends to be the more liquid.

European options are typically valued using the Black-Scholes or Black 76 formula. (This is a simple equation with a closed-form solution around which the financial community has standardized.) American options are impossible to value exactly, and 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).

If an American and a European option are otherwise identical (having the same strike price, etc) the American will be worth at least as much as the European option (which it contains). The American-style contract may be worth more than the European, and if so, the difference is some guide to the likelihood of early exercise. (This difference is often calculated directly as a spread of the American's value over the Black-Scholes price of the European in a numerical tactic to calibrate the more complex model against the European called the control variate technique.)

To account for the American's higher value there must be some situations in which it is optimal to exercise the American option before maturity. This can arise in several ways, such as:

  • An in the money (ITM) call option on a stock is often exercised just before the stock pays a dividend which would lower its value, taking the option on it out of the money
  • 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.
  • An american bond option on the dirty price of a bond (such as some convertible bonds) may be exercised immediately if ITM and a coupon is due.
  • 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).

Non-Vanilla Exercise Rights

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 bermudan option 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 bermudan style.
  • A capped-style option 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 compound option 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 shout option 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.

"Exotic" Options with Standard Exercise Styles

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 cross option (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 $MAX(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 quanto option 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).

Non-vanilla path dependent "exotic" options

The following "exotic options" are still options, but have pay offs 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 lookback option 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 asian option 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 russian option 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 game option 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 parisian option is dependent of the amount of time the option has spent above or below a strike price.
  • A Barrier option 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 binary option (also known as a digital option) pays a fixed amount, or nothing at all, depending o the price of the underlying instrument at maturity.

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