Special features used in derivatives
Many derivatives of all types use multipliers as ways of increasing leverage. An interest-rate swap, for example, many provide that the party agreeing to pay a floating rate will pay not libor plus 2 percentage points but rather the square of libor minus 5%. Under this arrangement, if floating rates drop the square of (libor 5%) will plummet and the owner’s payments will diminish rapidly. However, a small increase in floating rates could cause a sharp increase in the square of (libor 5%), and the owner of the floating rate position could owe significantly higher interest payments. Many of the large reported losses on derivatives transactions have come about because of multipliers of this sort embedded in the derivatives.
Another common arrangement in derivatives is a path-dependent option. Unlike a regular option, which pays off only if it is in the money at expiration (in the case of a European-style option) or when exercised before expiration (in the case of an American-style option), a path dependent option has a pay-off that depends on its behaviour throughout its life. A simple path-dependent currency derivative might pay off only if the euro trades above $1.20 for seven of the 14 days before expiration. A more complex variant could conceivably require that the euro trades above $1.15 on July 1st, above $1.175 on October 1st and above $1.20 on January 1st; unless all three of these conditions are met, the exchange rate will not have followed the agreed path and the owner will not receive a payment.
Pricing derivatives
As with exchange-traded options, the prices of over-the-counter derivatives are determined mainly by mathematical models. The factors affecting prices are much the same: the level of risk-free interest rates; the volatility of the underlying; expected changes in the price of the underlying; and time to expiration. Imagine a simple interest-rate swap, in which a manufacturing company wishes to exchange payments on $1m of debt floating at libor 3% for a fixed payment and an insurance company wishes to swap a 7% fixed-rate payment on $1m of principal for a floating rate. Before engaging in such a transaction each party, whether on its own or with the help of outside advisers, must develop a view of the likely course of interest rates over the relevant period. If they both judge that rates are likely to drop significantly, they may agree that over time the holder of the floating- rate position will probably pay less than the holder of the fixed position, so the insurer would pay a premium to the manufacturer in order to obtain the position it expects to be less costly. If they both think that interest rates will rise, they may agree that the manufacturer should pay a premium to the insurer for the opportunity to lock in a fixed rate. The precise amount of premium one party demands and the other agrees to pay will depend upon their estimates of the probable pay-offs until the derivative expires. For “plain vanilla” derivatives, such as a simple swap, there is a large and liquid market and little disagreement about pricing. For more com-plicated derivatives premiums can be harder to calculate. In some cases, the premium can be determined by disaggregating one derivative product into several simpler ones and summing the prices. Many customers, even sophisticated companies, have difficulty reckoning a fair price for highly complex derivatives. They often rely on the pricing models of their bankers, which can lead to upset if, as often happens, the derivative does not perform precisely as the model expected. Many users are required to account for their derivative positions at current market value at the end of each quarter, booking a gain or a loss if the instrument has changed in value. Values, which are best described by the price at which the instrument could be sold, are often provided by banks, and unanticipated price drops can force owners to book losses. The price a bank or other dealer will charge for a particular derivative will depend partly on the structure of the many derivative positions on the dealer’s books. Dealers generally seek to minimise the risks of derivatives by hedging their own positions. They can hedge a derivative by buying an offsetting derivative from another dealer or by arranging a transaction with another customer. A dealer may offer a favourable price for a derivative that exposes it to loss if oil prices rise if it already holds aderivative exposing it to loss if oil prices fall, as the combination of the two positions would leave it in a neutral position with regard to oil-price changes. A customer whose proposed transaction would increase the dealer’s risks might be offered a much less attractive price.
Another common arrangement in derivatives is a path-dependent option. Unlike a regular option, which pays off only if it is in the money at expiration (in the case of a European-style option) or when exercised before expiration (in the case of an American-style option), a path dependent option has a pay-off that depends on its behaviour throughout its life. A simple path-dependent currency derivative might pay off only if the euro trades above $1.20 for seven of the 14 days before expiration. A more complex variant could conceivably require that the euro trades above $1.15 on July 1st, above $1.175 on October 1st and above $1.20 on January 1st; unless all three of these conditions are met, the exchange rate will not have followed the agreed path and the owner will not receive a payment.
Pricing derivatives
As with exchange-traded options, the prices of over-the-counter derivatives are determined mainly by mathematical models. The factors affecting prices are much the same: the level of risk-free interest rates; the volatility of the underlying; expected changes in the price of the underlying; and time to expiration. Imagine a simple interest-rate swap, in which a manufacturing company wishes to exchange payments on $1m of debt floating at libor 3% for a fixed payment and an insurance company wishes to swap a 7% fixed-rate payment on $1m of principal for a floating rate. Before engaging in such a transaction each party, whether on its own or with the help of outside advisers, must develop a view of the likely course of interest rates over the relevant period. If they both judge that rates are likely to drop significantly, they may agree that over time the holder of the floating- rate position will probably pay less than the holder of the fixed position, so the insurer would pay a premium to the manufacturer in order to obtain the position it expects to be less costly. If they both think that interest rates will rise, they may agree that the manufacturer should pay a premium to the insurer for the opportunity to lock in a fixed rate. The precise amount of premium one party demands and the other agrees to pay will depend upon their estimates of the probable pay-offs until the derivative expires. For “plain vanilla” derivatives, such as a simple swap, there is a large and liquid market and little disagreement about pricing. For more com-plicated derivatives premiums can be harder to calculate. In some cases, the premium can be determined by disaggregating one derivative product into several simpler ones and summing the prices. Many customers, even sophisticated companies, have difficulty reckoning a fair price for highly complex derivatives. They often rely on the pricing models of their bankers, which can lead to upset if, as often happens, the derivative does not perform precisely as the model expected. Many users are required to account for their derivative positions at current market value at the end of each quarter, booking a gain or a loss if the instrument has changed in value. Values, which are best described by the price at which the instrument could be sold, are often provided by banks, and unanticipated price drops can force owners to book losses. The price a bank or other dealer will charge for a particular derivative will depend partly on the structure of the many derivative positions on the dealer’s books. Dealers generally seek to minimise the risks of derivatives by hedging their own positions. They can hedge a derivative by buying an offsetting derivative from another dealer or by arranging a transaction with another customer. A dealer may offer a favourable price for a derivative that exposes it to loss if oil prices rise if it already holds aderivative exposing it to loss if oil prices fall, as the combination of the two positions would leave it in a neutral position with regard to oil-price changes. A customer whose proposed transaction would increase the dealer’s risks might be offered a much less attractive price.
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