FINANCIAL DERIVATIVES

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FINANCIAL DERIVATIVES complete description....

[kiran51083]

FINANCIAL DERIVATIVES

A derivative instrument (or simply derivative) is a financial instrument which derives its value from the value of some other financial instrument or variable. For example, a stock option is a derivative because it derives its value from the value of a stock. An interest rate swap is a derivative because it derives its value from one or more interest rate indices. The value(s) from which a derivative derives its value is called its underlier(s).
By contrast, we might speak of primary instruments, although the term cash instruments is more common. A cash instrument is an instrument whose value is determined directly by markets. Stocks, commodities, currencies and bonds are all cash instruments. The distinction between cash and derivative instruments is not always precise, but it is a useful informal distinction.
Derivative instruments are categorized in various ways. One is the distinction between linear and non-linear derivatives. The former have payoff diagrams (The P&L from a long or short option position held to expiration is called the position's payoff. Payoff is a function of underlier value at expiration. It can be depicted with a graph, which is called a payoff diagram. ) that are linear or almost linear. The latter has payoff diagrams that are highly non-linear. Such non-linearity is always due to the derivative either being an option or having an option embedded in its structure.
A somewhat arbitrary distinction is between vanilla and exotic derivatives. The former tend to be simple and more common; the latter more complicated and specialized. There is no definitive rule for distinguishing one from the other, so the distinction is mostly a matter of custom. Usage does vary.

[kiran51083]

OPTIONS
An option is a contract, or a provision of a contract, that gives one party (the option holder) the right, but not the obligation, to perform a specified transaction with another party (the option issuer or option writer) according to specified terms. The owner of a property might sell another party an option to purchase the property any time during the next three months at a specified price. A lease might contain a provision granting the renter the option to extend the lease for an additional year. A corporate bond might have an option provision allowing the issuer to purchase the bond back from the purchaser five years prior to maturity for a specified price. A speculator might purchase an option to sell at any time during the next three months 100 shares of a particular stock for a specified price.
Option contracts are a form of derivative instrument. Stand-alone options trade on exchanges or OTC. They are linked to a variety of underliers. Most exchange-traded options have stocks or futures as underliers. OTC options have a greater variety of underliers, including bonds, currencies, physical commodities, swaps, or baskets of assets. Options can be embedded in almost any contract. Above, we gave examples of options embedded in a lease and a bond.
Options take many forms. The two most common are:
 Call options, which provide the holder the right to purchase an underlier at a specified price;
 Put options, which provide the holder the right to sell an underlier at a specified price.
The strike price of a call (put) option is the contractual price at which the underlier will be purchased (sold) in the event that the option is exercised. The last date on which an option can be exercised is called the expiration date. Options may allow for one of two forms of exercise:
 With American exercise, the option can be exercised at any time up to the expiration date.
 With European exercise, the option can be exercised only on the expiration date.
The origins of the names "American" and "European" in this context are unknown. They are unrelated to practices common in any particular geographic region.
A third form of exercise, which is occasionally used with OTC options, is Bermudan exercise. A Bermuda option can be exercised on a few specific dates prior to expiration. Yes, the name was chosen because Bermuda is half way between America and Europe.
As an example, consider a three-month, European exercise, strike USD 22.50 put option on 100,000 barrels of Brent oil. Such an option might trade OTC. It has:
 Underlier: Brent oil
 Notional amount: 100,000 barrels
 Expiration: in three months
 Strike price: USD 22.50
It gives the holder the right, but not the obligation, to sell the issuer 100,000 barrels of Brent oil three months from today, for a price of USD 22.50 per barrel.
Puts and calls are sometimes called vanilla options to distinguish them from more exotic structures.

[kiran51083]

VANILLA
A vanilla swap is any swap with fairly standardized provisions. The term is usually applied to vanilla interest rate swaps or vanilla currency swaps. Vanilla swaps are appealing because pricing tends to be transparent and transaction costs are small. Vanilla swaps can be used to speculate or to quickly hedge the market risk of a position without necessarily offsetting the specific cash flows of that position.
Swaps can also be customized to offset the specific cash flows of a position. Dealers often structure such non-vanilla swaps for clients. They may charge a fee for doing so, and pricing may reflect a large bid-ask spread (caveat emptor).

[kiran51083]

TYPES:
Option styles

the style or family of an 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 options are either European or American (style) options. These options - as well as others where the payoff is calculated similarly - are referred to as "vanilla options". Options where the payoff is calculated differently are categorised as "exotic options". Exotic options can pose challenging problems in valuation and hedging.
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.
Difference in value
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, 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:
• 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 by more than the option's remaining time value
• 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).

[kiran51083]

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 is between America and Europe). 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 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.

[kiran51083]

"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/Q-K,0), where Q is the prevailing FX rate. The pricing of such options naturally needs to take into account FX volatilty 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 £max(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.
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 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 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.

[kiran51083]

Call
A call option is a financial contract between two parties, the buyer and the seller of this type of option. Often it is simply labeled a "call". The buyer of the option has the right, but not the obligation to buy an agreed quantity of a particular commodity or financial instrument (the underlying instrument) from the seller of the option at a certain time (the expiration date) for a certain price (the strike price). The seller (or "writer") is obligated to sell the commodity or financial instrument should the buyer so decide. The buyer pays a fee (called a premium) for this right.
The buyer of a call option wants the price of the underlying instrument to rise in the future; the seller either expects that it will not, or is willing to give up some of the upside (profit) from a price rise in return for (a) the premium (paid immediately) plus (b) retaining the opportunity to make a gain up to the strike price (see below for examples).
Call options are most profitable for the buyer when the underlying instrument is moving up, making the price of the underlying instrument closer to the strike price. When the price of the underlying instrument surpasses the strike price, the option is said to be "in the money."
The initial transaction in this context (buying/selling a call option) is not the supplying of a physical or financial asset (the underlying instrument). Rather it is the granting of the right to buy the underlying asset, in exchange for a fee - the option price or premium.
Exact specifications may differ depending on option style. A European call option allows the holder to exercise the option (i.e., to buy) only on the option expiration date. An American call option allows exercise at any time during the life of the option.
Call options can be purchased on many financial instruments other than stock in a corporation - options can be purchased on futures on interest rates, for example (see interest rate cap) - as well as on commodities such as gold or crude oil. A call option should not be confused with either Incentive stock options or with a warrant. An incentive stock option, the option to buy stock in a particular company, is a right granted by a corporation to a particular person (typically executives) to purchase treasury stock. When an incentive stock option is exercised, new shares are issued. Incentive stock options are not traded on the open market. In contrast, when a call option is exercised, the underlying asset is transferred from one owner to another.

[kiran51083]

Example of a call option on a stock
• An investor buys a call on Microsoft Corporation stock with a strike price of $50 and an option expiration date of June 16 2006, and pays a premium of $5 for this call option. The current price is $40.
• Assume that the share price (the spot price) rises, and is $60 on the strike date. The investor would exercise the option (i.e., buy the share from the counter-party), and could then hold the share, or sell it in the open market for $60. The profit would be $10 minus the fee paid for the option, $5, for a net profit of $5. The investor has thus doubled his money, having paid $5, and ending up with $10.
• If however the share price never rises to $50 (that is, it stays below the strike price) up through the exercise date, then the option would expire as worthless. The investor loses the premium of $5.
• Thus, in any case, the loss is limited to the fee (premium) initially paid to purchase the stock, while the potential gain is theoretically unlimited (consider if the share price rose to $100).
• From the viewpoint of the seller, if the seller thinks the stock is a good one, he/she is $5 better (in this case) by selling the call option, should the stock in fact rise. However, the strike price (in this case, $50) limits the seller's profit. In this case, the seller does realize the profit up to the strike price (that is, the $10 rise in price, from $40 to $50, belongs entirely to the seller of the call option), but the increase in the stock price thereafter goes entirely to the buyer of the call option.
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From the above, it is clear that a call option has positive monetary value when the underlying instrument has a spot price (S) above the strike price (K). Since the option will not be exercised unless it is "in-the-money", the payoff for a call option is
Max[(S - K);0] or formally, (S - K) +
where
Prior to exercise, the option value, and therefore price, varies with the underlying price and with time. The call price must reflect the "likelihood" or chance of the option "finishing in-the-money". The price should thus be higher with more time to expiry (except in cases when a significant dividend is present), and with a more volatile underlying instrument. The science of determining this value is the central tenet of financial mathematics. The most common method is to use the Black-Scholes formula. Whatever the formula used, the buyer and seller must agree on the initial value (the premium), otherwise the exchange (buy/sell) of the option will not take place.

[kiran51083]

Put
A put option (sometimes simply called a "put") is a financial contract between two parties, the buyer and the writer of the option. The put allows the buyer the right but not the obligation to sell a commodity or financial instrument (the underlying instrument) to the writer of the option for a certain time for a certain price (the strike price). The writer has the obligation to purchase the underlying asset at that strike price, if the buyer exercises the option.
Note that the writer of the option is agreeing to buy the underlying asset if the put holder exercises the option. In exchange for having this option, the buyer pays the writer a fee (the premium). (Note: Although option writers are frequently referred to as sellers, because they initially sell the option that they create, thus, taking a short position in the option, they are not the only sellers. An option holder can also sell his long position in the option. However, the difference between the two sellers is that the option writer takes on the legal obligation to buy the underlying asset at the strike price, whereas, the option holder is merely selling his long position, and is not contractually obligated by the sold option.)
Exact specifications may differ depending on option style. A European put option allows the holder to exercise the put option for a short period of time right before expiration. An American put option allows exercise at any time during the life of the option.
The most widely-known put option is for stock in a particular company. However, options are traded on many other assets: financial - such as interest rates (see interest rate floor) - and physical, such as gold or crude oil.
The buyer of the put either expects the price of the underlying asset to fall or to protect a long position in the asset. The advantage of buying a put over shorting the asset is that the risk is limited to the premium. The put writer does not expect the price of the underlying to fall, and so writes the put to collect the premium. Puts can also be used to limit portfolio risk, and may be part of an option spread.
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Example of a put option on a stock
• I purchase a put contract to sell 100 shares of XYZ Corp. for $50. The current price is $55, and I pay a premium of $5. If the price of XYZ stock falls to $40 per share right before expiration, then I can exercise my put by buying 100 shares for $4,000, then selling it to a put writer for $5,000. My total profit would equal $500 ($5,000 from put writer - $4,000 for buying the stock - $500 for buying the put contract of 100 shares at $5 per share, excluding commissions).
• If, however, the share price never drops below the strike price (in this case, $50), then I would not exercise the option. (Why sell a stock to someone at $50, the strike price, if it would cost me more than that to buy it?) My option would be worthless and I would have lost my whole investment, the fee (premium) for the option contract, $500 ($5 per share, 100 shares per contract). My total loss is limited to the cost of the put premium plus the sales commission to buy it.
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This example illustrates that the put option has positive monetary value when the underlying instrument has a spot price (S) below the strike price (K). Since the option will not be exercised unless it is "in-the-money", the payoff for a put option is
max[ (K − S) ; 0 ] or formally, (K - S) +
where :
Prior to exercise, the option value, and therefore price, varies with the underlying price and with time. The put price must reflect the "likelihood" or chance of the option "finishing in-the-money". The price should thus be higher with more time to expiry, and with a more volatile underlying instrument. The science of determining this value is the central tenet of financial mathematics. The most common method is to use the Black-Scholes formula. Whatever the formula used, the buyer and seller must agree this value initially.

[Pushkar]

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