Derivatives

Introduction :

Derivatives are financial instruments whose value changes in response to the changes in underlying variables. The main types of derivatives are futures, forwards, options, and swaps

A financial instrument whose characteristics and value depend upon the characteristics and value of an underlier, typically a commodity, bond, equity or currency. Examples of derivatives include futures and options. Advanced investors sometimes purchase or sell derivatives to manage the risk associated with the underlying security, to protect against fluctuations in value, or to profit from periods of inactivity or decline. These techniques can be quite complicated and quite risky.

The emergence of the market for derivative products, most notably forwards, futures and options, can be traced back to the willingness of risk-averse economic agents to guard themselves against uncertainties arising out of fluctuations in asset prices. By their very nature, the financial markets are marked by a very high degree of volatility.

Types of derivatives:

Following re major types of financial derivatives;

Forwards:

A forward contract is a customized contract between two entities, where settlement takes place on a specific date in the future at today's pre-agreed price.

A Forward Contract is a way for a buyer or a seller to lock in a purchasing or selling price for an asset, with the transaction set to occur in the future. In essence, it is a financial contract obligating the buyer to buy, and the seller to sell a given asset at a predetermined price and date in the future. No cash or assets are exchanged until expiry, or the delivery date of the contract. On the delivery date, forward contracts can be settled by physical delivery of the asset or cash settlement.

Forward contjracts are very similar to futures contracts, except they are not marked to market, exchange traded, or defined on standardized assets. Forward contracts trade over the counter (OTC), thus the terms of the deal can be customized to fit the needs of both the buyer and the seller. However, this also means it is more difficult to reverse a position, as the counterparty must agree to canceling the contract, or you must find a third party to take an offsetting position in. This also increases credit risk for both parties.

Futures:

 A futures contract is an agreement between two parties to buy or sell an asset at a certain time in the future at a certain price. Futures contracts are special types of forward contracts in the sense that the former are standardized exchange-traded contracts.

Futures can be used either to hedge or to speculate on the price movement of the underlying asset. For example, a producer of corn could use futures to lock in a certain price and reduce risk (hedge). On the other hand, anybody could speculate on the price movement of corn by going long or short using futures.

Options:

Option contracts give trade hedgers and investors a more flexible alternative to futures as a means of trading on the Exchange. When buying an options contract, the purchaser (taker) is not entering into a firm obligation. They are simply buying a choice of action. This choice allows the genuine trade hedger the opportunity of locking in a fixed price while maintaining the ability to abandon the option in order to take advantage of favourable price movements. This would be forfeited with a straight futures hedge.

A call option is a contract giving its owner the right but not the obligation to buy an  futures contract(s) at a fixed price (strike price) at any time on or before a given date.

A put option is a contract giving its owner the right but not the obligation to sell and  futures contract(s) at a fixed price (strike price) at any time on or before a given date.

The cost of purchasing the option is referred to as the premium and, unless the option is traded on, this is a write-off. It is not part of the value of the underlying futures contract. This means it is down to the user's perception of the market and the cost of the option as to whether they choose to use futures or options as their hedging medium.

Swaps:

Swaps are private agreements between two parties to exchange cash flows in the future according to a prearranged formula. A kind of financial transaction which has many variations, usually highly complex. They generally involve a simultaneous exchange of assets (the swap) by counterparties for other different assets of comparable value. The assets may be commodities or they may be financial instruments involving interest rates, cash flows, foreign exchange, debts or equities. In addition to financial profits, the swaps have many purposes such as limiting risks, overcoming restrictions in certain markets, or balancing portfolios.

They can be regarded as portfolios of forward contracts. The two commonly used swaps are:

•           Interest rate swaps: 

An interest rate swap is a contractual agreement entered into between two counterparties under which each agrees to make periodic payment to the other for an agreed period of time based upon a notional amount of principal. The principal amount is notional because there is no need to exchange actual amounts of principal in a single currency transaction: there is no foreign exchange component to be taken account of. Equally, however, a notional amount of principal is required in order to compute the actual cash amounts that will be periodically exchanged.

Under the commonest form of interest rate swap, a series of payments calculated by applying a fixed rate of interest to a notional principal amount is exchanged for a stream of payments similarly calculated but using a floating rate of interest. This is a fixed-for-floating interest rate swap. Alternatively, both series of cash flows to be exchanged could be calculated using floating rates of interest but floating rates that are based upon different underlying indices. Examples might be Libor and commercial paper or Treasury bills and Libor and this form of interest rate swap is known as a basis or money market swap.

If we consider the generic fixed-to-floating interest rate swap, the most obvious difficulty to be overcome in pricing such a swap would seem to be the fact that the future stream of floating rate payments to be made by one counterparty is unknown at the time the swap is being priced. This must be literally true: no one can know with absolute certainty what the 6 month US dollar Libor rate will be in 12 months time or 18 months time. However, if the capital markets do not possess an infallible crystal ball in which the precise trend of future interest rates can be observed, the markets do possess a considerable body of information about the relationship between interest rates and future periods of time.

In many countries, for example, there is a deep and liquid market in interest bearing securities issued by the government. These securities pay interest on a periodic basis, they are issued with a wide range of maturities, principal is repaid only at maturity and at any given point in time the market values these securities to yield whatever rate of interest is necessary to make the securities trade at their par value.

At  any time the market is prepared to quote an investor forward interest rates. If, for example, an investor wishes to place a sum of money on deposit for six months and then reinvest that deposit once it has matured for a further six months, then the market will quote today a rate at which the investor can re-invest his deposit in six months time. This is not an exercise in "crystal ball gazing" by the market. On the contrary, the six month forward deposit rate is a mathematically derived rate which reflects an arbitrage relationship between current (or spot) interest rates and forward interest rates. In other words, the six month forward interest rate will always be the precise rate of interest which eliminates any arbitrage profit. The forward interest rate will leave the investor indifferent as to whether he invests for six months and then re-invests for a further six months at the six month forward interest rate or whether he invests for a twelve month period at today's twelve month deposit rate.

The graphical relationship of forward interest rates is known as the forward yield curve. One must conclude, therefore, that even if -- literally -- future interest rates cannot be known in advance, the market does possess a great deal of information concerning the yield generated by existing instruments over future periods of time and it does have the ability to calculate forward interest rates which will always be at such a level as to eliminate any arbitrage profit with spot interest rates. Future floating rates of interest can be calculated, therefore, using the forward yield curve but this in itself is not sufficient to let us calculate the fixed rate payments due under the swap. A further piece of the puzzle is missing and this relates to the fact that the net present value of the aggregate set of cash flows due under any swap is -- at inception -- zero. The truth of this statement will become clear if we reflect on the fact that the net present value of any fixed rate or floating rate loan must be zero when that loan is granted, provided, of course, that the loan has been priced according to prevailing market terms. This must be true, since otherwise it would be possible to make money simply by borrowing money, a nonsensical result However, we have already seen that a fixed to floating interest rate swap is no more than the combination of a fixed rate loan and a floating rate loan without the initial borrowing and subsequent repayment of a principal amount. The net present value of both the fixed rate stream of payments and the floating rate stream of payments in a fixed to floating interest rate swap is zero, therefore, and the net present value of the complete swap must be zero, since it involves the exchange of one zero net present value stream of payments for a second net present value stream of payments.

•           Currency swaps:

Currency swaps are agreements between two individuals or entities to exchange specified types and amounts of currencies. Along with the initial exchange of a specific amount of one currency for a specific amount of a different currency, the process of a currency swap normally also includes a series of recurring payments based on the cash flow performance of the two currencies. This makes a currency swap somewhat different from a currency, in that the exchange normally involves simply exchanging currency at the most recent rate of exchange.

The recurring payments that compose the second phase of a currency swap normally make use of both fixed and variable rates of interest. One party will agree to pay a fixed interest rate, while the second party will make interest payments based on a floating rate of exchange. However, it is possible to arrange a currency swap agreement where both parties pay recurring payments based on a fixed rate or a floating exchange rate. The final determination of how the interest rate will be calculated is defined in the terms and conditions that govern the swap.

One important aspect of the currency swap that also sets it apart from currency exchanges is the fact that the swapping of the currency is not a permanent component. At the time that the two currencies are swapped, the parties agree to make the recurring interest rate payments for a specific period of time. Once the duration outlined in the agreement is complete, the two currencies are returned to the original owner. However, each party retains all returns that were shared in the form of interest payments.

The transaction of a currency swap is usually utilized when there is some expectation that the two currencies in question have potential to realize a significant amount of return via the rates of interest accrued. As can be expected, both parties usually anticipate realizing a higher return with the currency type that is received in theswap. However, since rates of exchange tend to fluctuate over time, there is usually a reasonable chance that both parties ultimately benefit from the currency swap.

Warrants:

It is a security that entitles the holder to buy stock of the issuing company at a specified price, which can be higher or lower than the stock price at time of issue.

Warrants and options are similar in that the two contractual financial instruments allow the holder special rights to buy securities. Both are discretionary and have expiration dates. The word warrant simply means to "endow with the right", which is only slightly different to the meaning of an option.

Warrants are frequently attached to bonds or preferred stock as a sweetener, allowing the issuer to pay lower interest rates or dividends. They can be used to enhance the yield of the bond, and make them more attractive to potential buyers. Warrants can also be used in private equity deals. Frequently, these warrants are detachable, and can be sold independently of the bond or stock.

In the case of warrants issued with preferred stocks, stockholders may need to detach and sell the warrant before they can receive dividend payments. Thus, it is sometimes beneficial to detach and sell a warrant as soon as possible so the investor can earn dividends.

Options generally have lives of up to one year, the majority of options traded on options exchanges having a maximum maturity of nine months. Longer-dated options are called warrants and are generally traded over-the-counter.

LEAPS:

The acronym LEAPS means Long-Term Equity Anticipation Securities. These are options having a maturity of up to three years.

In finance, LEAPS  are options of longer term until expiry than other, more common, options. LEAPS are available on approximately 2500 equities and 20 indexes. As with traditional short term options, LEAPS are available in two forms, calls and puts.

Options were originally created with expiry cycles of 3, 6, and 9 months, with no option term lasting more than a year. Options of this form, for such terms, still constitute the vast majority of options activity. LEAPS were created relatively recently and typically extend for terms of 2 years out. Equity LEAPS always expire in January. For example, if today were November 2005, one could buy a Microsoft January call option that would expire in 2006, 2007, or 2008. (The further out the expiration date, the more expensive the option.) The latter two are LEAPS.

When LEAPS were first introduced in 1990, they were derivative instruments solely for equities; however, more recently, equivalent instruments for indices have become available. These are also referred to as LEAPS.

LEAPS are an excellent way for a longer-term trader to gain exposure to a prolonged trend in a given security without having to roll several short-term contracts together. The ability to buy a call/put option that expires one or two years in the future is very alluring because it gives the holder exposure to the long-term price movement without the need to invest the larger amount of capital that would be required to own the underlying asset outright. These long-term options can be purchased not only for individual stocks, but also for equity indexes (such as the S&P 500).

Baskets: Basket options are options on portfolios of underlying assets. The underlying asset is usually a moving average or a basket of assets. Equity index options are a form of basket options.

A basket option is an option whose payoff is linked to a portfolio or "basket" of underlier values. The basket can be any weighted sum of underlier values so long as the weights are all positive. Basket options are usually cash settled. A call option on France's CAC 40 stock index is an example of a basket option.

Basket options are popular for hedging foreign exchange risk. A corporation with multiple currency exposures can hedge the combined exposure less expensively by purchasing a basket option than by purchasing options on each currency individually.

Basket options are often priced by treating the basket's value as a single underlie and applying standard option pricing formulas. An error is introduced by the fact that a weighted sum of lognormal random variables in not lognormal, but this is generally modest.

Swaptions:

Swaptions are options to buy or sell a swap that will become operative at the expiry of the options. Thus a swaption is an option on a forward swap. Rather than have calls and puts, the swaptions market has receiver swaptions and payer swaptions. A receiver swaption is an option to receive fixed and pay floating. A payer swaption is an option to pay fixed and receive floating.

Swaptions can be for American, European or Bermudan exercise. They can be physically settled, in which case an option is actually entered into upon exercise. They can also be cash settled, in which case the market value of the underlying swap changes hands upon exercise.

To specify a swaption, we must indicate three things:

•           the expiration date of the option

•           the fixed rate on the underlying swap

•           the tenor (time to maturity at exercise of the option) of the swap.

The purchaser of the swaption pays an upfront premium. If she exercises, there is no strike price to pay. The two parties simply put on the prescribe swap. Note, however, the fixed rate specified for the swaption plays a role very similar to that of a strike price. The holder of the swaption will decide whether or not to exercise based on whether swap rates rise above or fall below that fixed rate. For this reason, the fixed rate is often called the strike rate.

By symmetry, a call on a pay-fixed swap is the same thing as aput on a receive-fixed swap. Similarly, a call on a receive fixed swap is the same as a put on a pay fixed swap. For this reason, it is often more convenient to speak in terms of two basic forms of swaption:

•           A payer swaption is a call on a pay-fixed swap the swaption holder has the option to pay fixed on a swap.

•           A receiver swaption is a call on a receive fixed swap, the swaption holder has the option to receive fixed on a swap.