The Mathematics of Financial Modelingand Investment Management

20-Term Structure Page 610 Wednesday, February 4, 2004 1:33 PM

610 The Mathematics of Financial Modeling and Investment Management

The convention in the swap market is to quote the reference rate flat

(i.e., no spread) and quote the fixed-rate side as a spread over a bench-

mark (typically the yield on a government bond) with the same maturity

as the swap.

Effectively the swap rate reflects the risk of the counterparty to the

swap failing to satisfy its obligation. Consequently, the swap curve does

not reflect rates for a default-free obligation. Instead, the swap curve

reflects credit risk. Since the counterparty in swaps are typically bank-

related entities, the swap curve reflects the credit risk of the banking sec-

tor—effectively, it is an interbank or AA rated curve.

Investors and issuers use the swap market for hedging and arbitrage

purposes, and the swap curve as a benchmark for evaluating performance

of fixed-income securities and the pricing of fixed-income securities. Since

the swap curve is effectively the LIBOR curve and investors borrow based

on LIBOR, the swap curve is more useful to funded investors than a gov-

ernment yield curve.

The increased application of the swap curve for these activities is

due to its advantages over using the government bond yield curve as a

benchmark. Before identifying these advantages, it is important to

understand that the drawback of the swap curve relative to the govern-

ment bond yield curve could be poorer liquidity. In such instances, the

swap rates would reflect a liquidity premium. Fortunately, liquidity is

not an issue in many countries as the swap market has become highly

liquid, with narrow bid-ask spreads for a wide range of swap maturities.

In some countries swaps may offer better liquidity than that country’s

government bond market. The advantages of the swap curve over a gov-

ernment bond yield curve are:^3

1. There is almost no government regulation of the swap market. The
   lack of government regulation makes swap rates across different
   markets more comparable. In some countries, there are some sover-
   eign issues that offer various tax benefits to investors and, as a
   result, for global investors it makes comparative analysis of govern-
   ment rates across countries difficult because some market yields do
   not reflect their true yield.


2. The supply of swaps depends only on the number of counterparties
   that are seeking or are willing to enter into a swap transaction at
   any given time. Since there is no underlying government bond, there

(^3) See Uri Ron, “A Practical Guide to Swap Curve Construction,” Chapter 6 in Frank
J. Fabozzi (ed.), Interest Rate, Term Structure, and Valuation Modeling (New York:
John Wiley & Sons, 2002).