Derivatives and Options

This is just a place to stick the notes that I am currently making about options.
If anyone reading this wishes to comment in any way, please feel free.
Much of this stuff is ripped from wikipedia, although there are some original notes.


Derivatives
A derivative instrument is a contract between two parties that specifies conditions (especially the dates, resulting values of the underlying variables, and notional amounts) under which payments, or payoffs, are to be made between the parties.


Option style
American and European options
The key difference between American and European options relates to when the options can be exercised:
A European option may be exercised only at the expiry date 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 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 exchanges are mainly American-style, whereas those traded over-the-counter are mainly European.
Nearly all stock and equity options are American options, while indexes are generally represented by European options. A list of European and American options can be found on the Options Industry Council website.


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. This is intermediate between a European option—which allows exercise at a single time, namely expiry—and an American option, which allows exercise at any time (the name is a pun: Bermuda, a British overseas territory, is somewhat American and somewhat European - in terms of both option style and physical location - but is nearer to American in terms of both). 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); see Swaption: Valuation. Most exotic interest rate options are of Bermudan style.
A Canary option is an option whose exercise style lies somewhere between European options and Bermudan options. (The name refers to the relative geography of the Canary Islands.) Typically, the holder can exercise the option at quarterly dates, but not before a set time period (typically one year) has elapsed. The term was coined by Keith Kline, who at the time was an agency fixed income trader at the Bank of New York.
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.
A swing option gives the purchaser the right to exercise one and only one call or put on any one of a number of specified exercise dates (this latter aspect is Bermudan). Penalties 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.


"Exotic" options with standard exercise styles
These options can be exercised either European style or American style; they differ from the plainvanilla option only in the calculation of their pay-off value:
A cross option (or composite option) is an option on some underlying asset 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 JPYMAX(S/Q-K,0), where Q is the prevailing FX rate. The pricing of such options naturally needs to take into account FX volatility and the correlation between the exchange rate of the two currencies involved and the underlying stock price.
A quanto option is a cross option in which the exchange rate is fixed at the outset of the trade, typically at 1. The payoff of an IBM quanto call option would then be JPYmax(S-K,0).
An exchange option is the right to exchange one asset for another (such as a sugar future for a corporate bond).
A basket option is an option on the weighted average of several underlyings
A rainbow option is a basket option where the weightings depend on the final performances of the components. A common special case is an option on the worst-performing of several stocks.
A Low Exercise Price Option (LEPO) is a European style call option with a low exercise price of $0.01.


Non-vanilla path dependent "exotic" options
The following "exotic options" 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 lookback option is a path dependent option where the option owner has the right to buy (sell) the underlying instrument at its lowest (highest) price over some preceding period.
An Asian option (or Average 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). Asian options were originated in Asian markets to prevent option traders from attempting to manipulate the price of the underlying security on the exercise date.[citation needed]
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 Cumulative Parisian option is dependent on the total amount of time the underlying asset value has spent above or below a strike price.
The payoff of a Standard Parisian option is dependent on the maximum amount of time the underlying asset value has spent consecutively above or below a strike price.
A barrier option involves a mechanism where if a 'limit price' is crossed by the underlying, the option either can be exercised or can no longer be exercised.
A double barrier option involves a mechanism where if either of two 'limit prices' is crossed by the underlying, the option either can be exercised or can no longer be exercised.
A Cumulative Parisian barrier option involves a mechanism where if the total amount of time the underlying asset value has spent above or below a 'limit price', the option can be exercised or can no longer be exercised.
A Standard Parisian barrier option involves a mechanism where if the maximum amount of time the underlying asset value has spent consecutively above or below a 'limit price', the option can be exercised or can no longer be exercised.
A reoption occurs when a contract has expired without having been exercised. The owner of the underlying security may then reoption the security.
A binary option (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 chooser option gives the purchaser a fixed period of time to decide whether the derivative will be a vanilla call or put.
A forward start option is an option whose strike price is determined in the future
A cliquet option is a sequence of forward start options


Notes:


Barrier options
In finance, a barrier option is a financial derivative which either springs into existence upon the occurrence of the event of the price of the underlying asset breaching a barrier (in the case of "up and in" and "down and in" options) or whose existence is extinguished upon the occurrence of the event of the price of the underlying asset breaching a barrier (in the case of an "up and out" or a "down and out"). Most often this contingent derivate is an option on the underlying asset whose price breaching the pre-set barrier level either springs the option into existence or extinguishes an already existing option. Barrier options are always cheaper than a similar option without barrier. Barrier options were created to provide the insurance value of an option without charging as much premium. For example, if you believe that IBM will go up this year, but are willing to bet that it won't go above $200, then you can buy the barrier and pay less premium than the vanilla option.


Strike Price
The Strike price is the value of the underlying that the option gives you the right to exercise. The spot price is the value of the underlying asset. The two are not necessarily related. Both of these prices are different to the actual price of the option.


For example, I buy an option to buy 1 ounce of gold in one month at $1666, this is the strike price.


A month passes and  the option expires. At the time of expiry, gold is worth $1700. Therefore, you exercise the option and make $334


Barrier options are complex financial instruments that are used to hedge against excessive risk. Barrier options have a 'barrier' which is a pre-selected value in the underlying asset. If the value of the underlying crosses that value, then it will trigger a 'barrier event' which, depending on the type of option, either summon the option into existence, or destroy it.


For instance, say I have bought a barrier option on gold at $1800, as long remains under that price, then the option will not triger, but as soon as it goes over that price, the option is called into existence, giving me the option to buy gold at $1600.


This is just a simple example. With some barrier options, the barrier is more complex, for instance, the barrier is taken as an average price on the underlying, this is known as an Asian Option.


A European Option may be exercised only on the expiry date, whereas an american option may be exercised at any point in time. This is a small, but crucial difference as European options will be primarily aimed at strategies where the option can be successfully pursued only on the expiry date, whereas an american option could be used to take advantage of an exceptional swing in the value of the underlying due to market volatility. Some options are called Bermudan, which means that through the life of the option, there are a number of discreet days during the life of the option when the owner may exercise 


Because an American option can be cashed at any time, they more expensive than european options. Just how expensive is determined by the likelihood that the option will be exercised before maturity.


Look into options, possibly barrier options as a way to insure against market swings. Options, particularly barrier options are much cheaper than buying the underlying, and once activated, give one an option to buy the underlying at a very attractive price when can help hedge against market uncertainty.


Although the above only really applies if one is an owner or forced buyer of the underlying, for instance an air carrier that must buy fuel in order to function. Barrier options could be a very good way of insuring against wild market swings. I would suspect that the cost of the option would be related to the likelihood of it being activated and hence the likelihood of large swings in the underlying.


Christopher Carrion