U
NIVERSITY OF
E
SSEX
D
EPARTMENT OF
E
CONOMICS
Term Structure of Interest Rates
Yield curves
Yield curves show the relationship between
spot yield
and
time to maturity
(i.e. ‘life’) of
a bond.
Spot yield
:
y
n,t
≡
(
m/p
n,t
)
(1
/n
)

1
is the yield to maturity on a Zero Coupon (pure discount)
bond with life
n
at date
t
, where
p
n,t
is the market price of the bond at date
t
and
m
is its
face value.
From now on all bonds are assumed to be Zero Coupon.
Theories of the term structure seek to explain the shape of the yield curve at each date.
Implicit forward rates
Implicit forward rates are future yields (interest rates) implied by today’s observed bond
yields.
Define
n

1
f
n
as the implied rate between dates
n

1
and
n
as of today,
t
:
(1 +
y
n

1
)
n

1
(1 +
n

1
f
n
) = (1 +
y
n
)
n
(1)
All the above are defined as of today, i.e. should have an extra
t
subscript.
The term structure (yield curves) can equivalently be expressed using implicit forward rates,
rather than spot yields.
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 Spring '12
 R.E.Bailey
 Interest Rates, Yield Curve, expectations hypothesis, Bond Yields, future bond yields

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