The Mathematics of Financial Modelingand Investment Management

2-Financial Markets Page 71 Wednesday, February 4, 2004 1:15 PM

Overview of Financial Markets, Financial Assets, and Market Participants 71

In general, the payment made by the seller of the cap to the buyer

on a specific date is determined by the relationship between the desig-

nated reference and the strike. If the former is greater that the latter,

then the seller pays the buyer:

Notional principal amount × [Actual value of designated reference – Strike]

If the designated reference is less than or equal to the strike, then the

seller pays the buyer nothing.

For a floor, the payment made by the seller to the buyer on a specific

date is determined as follows. If the designated reference is less than the

strike, then the seller pays the buyer:

Notional principal amount × [Strike – Actual value of designated reference]

If the designated reference is greater than or equal to the strike, then the

seller pays the buyer nothing.

In a cap or floor, the buyer pays a fee which represents the maxi-

mum amount that the buyer can lose and the maximum amount that the

seller of the agreement can gain. The only party that is required to per-

form is the seller. The buyer of a cap benefits if the designated reference

rises above the strike because the seller must compensate the buyer. The

buyer of a floor benefits if the designated reference falls below the strike

because the seller must compensate the buyer.

In essence the payoff of these contracts is the same as that of an

option. A call option buyer pays a fee and benefits if the value of the

option’s underlying asset (or equivalently, designated reference) is

higher than the strike price at the expiration date. A cap has a similar

payoff. A put option buyer pays a fee and benefits if the value of the

option’s underlying asset (or equivalently, designated reference) is less

than the strike price at the expiration date. A floor has a similar payoff.

An option seller is only entitled to the option price. The seller of a cap

or floor is only entitled to the fee. Thus, a cap and a floor can be viewed

as simply a package of options. As with a swap, a complex contract can

be seen to be a package of basic contracts (forward contracts in the case

of swaps and options in the case of caps and floors).

SUMMARY

■ The claims of the holder of a financial asset may be either a fixed dollar

amount (fixed income instrument or bond) or a varying, or residual,

amount (common stock).