The Mathematics of Financial Modelingand Investment Management

2-Financial Markets Page 70 Wednesday, February 4, 2004 1:15 PM

70 The Mathematics of Financial Modeling and Investment Management

counterparties swap payments in the same currency based on an interest

rate. For example, one of the counterparties can pay a fixed-interest rate

and the other party a floating interest rate. The floating-interest rate is

commonly referred to as the reference rate. In an interest rate-equity swap,

one party is exchanging a payment based on an interest rate and the other

party based on the return of some equity index. The payments are made in

the same currency. In an equity swap, both parties exchange payments in

the same currency based on some equity index. Finally, in a currency swap,

two parties agree to swap payments based on different currencies.

A swap is not a new derivative instrument. Rather, it can be decom-

posed into a package of forward contracts. While a swap may be nothing

more than a package of forward contracts, it is not a redundant contract

for several reasons. First, in many markets where there are forward and

futures contracts, the longest maturity does not extend out as far as that of

a typical swap. Second, a swap is a more transactionally efficient instru-

ment. By this we mean that in one transaction an entity can effectively

establish a payoff equivalent to a package of forward contracts. The for-

ward contracts would each have to be negotiated separately. Third, the

liquidity of some swap markets is now better than many forward con-

tracts, particularly long-dated (i.e., long-term) forward contracts.

CAPS AND FLOORS

There are agreements available in the financial market whereby one

party, for a fee (premium), agrees to compensate the other if a desig-

nated reference is different from a predetermined level. The party that

will receive payment if the designated reference differs from a predeter-

mined level and pays a premium to enter into the agreement is called the

buyer. The party that agrees to make the payment if the designated ref-

erence differs from a predetermined level is called the seller.

When the seller agrees to pay the buyer if the designated reference

exceeds a predetermined level, the agreement is referred to as a cap. The

agreement is referred to as a floor when the seller agrees to pay the

buyer if a designated reference falls below a predetermined level. The

designated reference could be a specific interest rate such as LIBOR or

the prime rate, the rate of return on some domestic or foreign stock

market index such as the S&P 500 or the DAX, or an exchange rate

such as the exchange rate between the U.S. dollar and the Japanese yen.

The predetermined level is called the strike. As with a swap, a cap and a

floor have a notional principal amount. Only the buyer of a cap or a

floor is exposed to counterparty risk.