TER
Interest
Rates
Interest rates are a factor in the valuation
of
virtually all derivatives and will feature
prominently in much
of
the material that
will
be presented in the rest
of
this book. In
this chapter
we
cover some fundamental issues concerned with the
way
interest rates are
measured and analyzed.
We
explain the compounding frequency used to define an
interest rate and the meaning
of
continuously compounded interest rates, which are
used extensively in the analysis
of
derivatives.
We
cover zero rates,
par
yields, and yield
curves, discuss bond pricing, and outline a procedure commonly used
by
a derivatives
trading desk to calculate zerocoupon Treasury interest rates.
We
cover forward rates
and forward rate agreements and review different theories
of
the term structure
of
interest rates.
Finally
we
explain the use
of
duration and convexity measures to
determine the sensitivity
of
bond prices to interest rate changes.
Chapter 6 will cover interest rate futures and show how the duration measure can be
used when interest rate exposures are hedged.
For
ease
of
exposition
we
will ignore day
count conventions throughout this chapter. The nature
of
these conventions and their
impact on
calculation~
will
be discussed in Chapters 6 and
7.
4.1
TYPES
OF
RATES
An interest rate in a particular situation defines the amount
of
money a borrower
promises to pay the lender.
For
any given currency, many different types
of
interest rates
are regularly quoted. These include mortgage rates, deposit rates, prime borrowing
rates, and
so
on. The interest rate applicable in a situation depends on the credit risk.
This
is
the risk that there will be a default by the borrower
of
funds, so that the interest
and principal are not paid to the lender as promised. The higher the credit risk, the
higher the interest rate that
is
promised by the borrower.
Treasury Rates
Treasury rates are the rates an investor earns on Treasury bills and Treasury bonds. These
are the instruments used by a government to borrow in its own currency. Japanese
Treasury rates are the rates at which the Japanese government borrows in
yen;
US
Treasury rates are the rates at which the US government borrows in US dollars; and so
75
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CHAPTER
4
on.
It
is
usually assumed that there
is
no chance that a government will default on an
obligation denominated in its own currency.l Treasury rates are therefore totally riskfree
rates in the sense that an investor who buys a Treasury bill or Treasury bond
is
certain
that interest and principal payments
will
be made as promised.
Treasury rates are important because they are used to price Treasury bonds and are
sometimes used to define the payoff from a derivative. However, derivatives traders
(particularly those active in the overthecounter market) do not usually use Treasury
rates as riskfree rates. Instead they use LIBOR rates.
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 Spring '11
 DonBlasius
 Math, Derivative, Interest Rates, Zerocoupon bond

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