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Option style
T
Redirected from Asian
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.
-
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).
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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.
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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).
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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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source:
http://en.wikipedia.org/wiki/Option_style
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