Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues

6

Swaps

6.1 DEFINITIONS AND FIRST EXAMPLES

Contractually speaking, a swap contract is an agreement between two parties to exchange a series of cash flows.1 Technically speaking, a swap is a set of successive forward transactions, involving either a fixed interest rate and a floating (or “variable”) rate, or two different floating rates, or, in the case of a CRS only, two different fixed rates. Fixed rates involved in swaps are called swap rates. Floating rates are based on the -ibor rates, prevailing two banking days before the beginning of the period they are applied to. Both the types of cash flows, being based on a fixed or on a floating rate, are paid at their respective maturity, and netted in case of common maturity dates.

Exchanged cash flows can be assets cash flows originating from assets payments, in this case one talk about asset swaps, or cash flows originating from debts interest payments, hence the naming of liability swaps.

If the whole set of exchanged cash flows involves a common single currency, the swap is called an interest rate swap (IRS). If the exchange of cash flows involves two currencies, one talks of currency rate swap (CRS) or cross currency rate swap (CCRS).2

A swap is an unconditional product: the exchange of cash flows cannot depend from any kind of condition. A contrario, credit default swaps and similar derivatives on a default risk are not swaps, strictly speaking, because there are conditional. We will look at these in Chapter 13.

The market ...