20-Term Structure Page 611 Wednesday, February 4, 2004 1:33 PM
Term Structure Modeling and Valuation of Bonds and Bond Options 611can be no effect of market technical factors that may result in the
yield for a government bond issue being less than its true yield.^4- Comparisons across countries of government yield curves is difficult
because of the differences in sovereign credit risk. In contrast, the
credit risk as reflected in the swaps curve are similar and make com-
parisons across countries more meaningful than government yield
curves. Sovereign risk is not present in the swap curve because, as
noted earlier, the swap curve is viewed as an interbank yield curve
or AA yield curve. - There are more maturity points available to construct a swap curve
than a government bond yield curve. More specifically, what is
quoted daily in the swap market are swap rates for 2-, 3-, 4-, 5-, 6-,
7-, 8-, 9-, 10-, 15-, and 30-year maturities. Thus, in the swap mar-
ket there are 10 market interest rates with a maturity of two years
and greater. In contrast, in the U.S. Treasury market, for example,
there are only three market interest rates for on-the-run Treasuries
with a maturity of two years or greater (2, 5, and 10 years) and one
of the rates, the 10-year rate, may not be a good benchmark because
it is often on special in the repo market. Moreover, because the U.S.
Treasury has ceased the issuance of 30-year bonds, there is no 30-
year yield available.
In the valuation of fixed-income securities, it is not the Treasury
yield curve that is used as the basis for determining the appropriate dis-
count rate for computing the present value of cash flows but the Trea-
sury spot rates. The Treasury spot rates are derived from the Treasury
yield curve using the bootstrapping process. Similarly, it is not the swap
curve that is used to for discounting cash flows when the swap curve is
the benchmark but the corresponding spot rates. The spot rates are
derived from the swap curve in exactly the same way—using the boot-
strapping methodology. The resulting spot rate curve is called the
LIBOR spot rate curve. Moreover, a forward rate curve can be derived
from the spot rate curve. The same thing is done in the swap market.
The forward rate curve that is derived is called the LIBOR forward rate
curve.
Consequently, if we understand the mechanics of moving from the
yield curve to the spot rate curve to the forward rate curve in the Trea-
sury market, there is no reason to repeat an explanation of that process
here for the swap market; that is, it is the same methodology, just differ-
ent yields are used.(^4) For example, a government bond issue being on “special” in the repurchase agree-
ment market.