The valuation of US Dollar interest rate swaps

BIS Economic Papers No 35
January 1993

Introduction

A swap is an agreement between two counterparties to exchange cash flows linked to two different indices at one or more dates in the future. Swaps have been used in conjunction with indices relating to interest and exchange rates as well as commodity and equity prices. With interest rate swaps, typically, the cash flows which are exchanged consist of interest payments having different characteristics but based on a common underlying or notional principal amount which in general is not exchanged. The most common ("plain vanilla") interest rate swap consists of one party undertaking payments linked to a short-term floating interest rate index such as LlBOR and receiving a stream of fixed interest payments; the other counterparty undertakes the opposite set of transactions. With currency swaps and commodity swaps the cash flows which are exchanged consist of payments indexed to interest rates (fixed or floating) in different currencies (and typically also include the exchange of the underlying principal amounts at maturity) and to prices of commodities respectively.

Since their inception in the early 1980s various types of swaps have come to dominate the markets for over-the-counter derivative instruments and to rival in size and depth those for futures contracts traded on organised exchanges. The key parties to swap transactions are commercial and investment banks, though probably all major financial market participants have been counterparties to some form of swap. Swaps have evolved from being initially linked to new issue activity in the capital markets, particularly the Euro-bond market, to being a more general instrument for financial risk management. This evolution has been accompanied by growing sophistication in the techniques utilised and by the development of new related financial instruments, such as caps, floors and swaptions. At the same time, the basic swap transactions have become increasingly standardised, with two-way prices for swaps of various maturities being quoted by major commercial and investment banks and posted by brokers.

The purpose of this paper is to examine the valuation or pricing of interest rate swaps, specifically in the US dollar market. The first section provides a brief overview of the structure of the interest rate swap market and summarises some of the explanations which have been given for its growth.

The second section describes the main features of standard interest rate swaps, the principal market conventions and the pricing relationships with other closely substitutable financial instruments. Swaps are derivative instruments and their pricing is bounded by that of other financial transactions. In particular, Euro-dollar futures and new issues of fixed interest rate bonds can be used to obtain a structure of interest rate payments similar to that offered by swaps. However, like many other derivative instruments, arbitrage pricing may be difficult or imperfect, with the result that risk elements enter the pricing of swaps. The third section considers several potential explanatory factors for the prices of swaps when arbitrage is not perfect.

The remainder of this study examines the relationship between the pricing of US dollar interest rate swaps and other financial variables. The fourth section describes the statistical properties of a sample of interest rate swap spreads with different maturities in order to compare them with those of other commonly traded financial instruments. The fifth section outlines a model for the pricing of swaps in terms of other economic variables and provides evidence on the different factors which influence the pricing of swaps with various maturities.