This preview shows pages 1–10. Sign up to view the full content.
1
10
Coupon Bonds
The chapter studies coupon bonds from the
perspective
of
the
arbitragefree
pricing
methodology.
This is in contrast to the classical approach to
fixed income analysis or coupon bond pricing
that was presented in Chapter 2.
The differences between the two approaches are
numerous.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 2
First, the arbitragefree pricing methodology can
be used to risk manage a portfolio of bonds given
an arbitrary evolution for the term structure of
interest rates. The classical approach can only
hedge parallel shifts in the term structure of
interest rates.
Second, the arbitragefree pricing approach can be
used to price interest rate derivatives in a manner
consistent with that used to price couponbonds.
The classical approach cannot.
Third, the arbitragefree pricing approach can be
extended to handle foreign currency risk and
credit risk.
The classical approach cannot.
3
A
A Coupon Bond as a Portfolio of ZeroCoupon
Bonds
This section studies the arbitragefree pricing of
noncallable coupon bonds.
The valuation method of this section is
independent of the particular evolution of the
term structure of interest rates selected; in
particular, it does not depend on the number or
specification of the factors in the economy, either
one, two, or three factors.
We define a
coupon bond
with principle L,
coupons C, and maturity T to be a financial
security that is entitled to receive coupon
payments of C dollars at times 1, …, T with a
principal repayment of L at time T.
The coupon rate on the bond is c = 1+C/L.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 4
Table 10.1:
The Cash Flows to a Typical
Coupon Bond with Price
B
(0), Principal L,
Coupon C and Maturity T
Time
012…
T


B
(0)
C
C
…
C
Coupons
LP
r
i
n
c
i
p
a
l
coupon rate c = 1+C/L
5
The coupon bond’s cash flows can be obtained
from a portfolio of zerocoupon bonds.
The duplicating portfolio consists of
C
zerocoupon bonds maturing at times
=
1
, .
.., T
1
and C+L zerocoupon bonds maturity at time T.
Let the market price of the coupon bond be
denoted
B(t)
.
The cost of constructing the duplicating portfolio
of zerocoupon bonds is:
)
T
,
t
(
LP
T
1
t
i
)
i
,
t
(
CP
+
∑
+
=
.
In constructing this portfolio, it is assumed that
the construction occurs after the coupon payment
has been paid at time
t
(i.e., it represents the
excoupon value at time
t
).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 6
Thus, the arbitragefree price of the coupon
bond is:
)
T
,
t
(
LP
T
1
t
i
)
i
,
t
(
CP
)
t
(
+
∑
+
=
=
B
.
(10.1)
Note that the arbitragefree price for the coupon
bond can be computed without any knowledge of
the evolution of the term structure of interest
rates.
It depends solely on the initial zerocoupon bond
price curve.
We now illustrate this computation
with an example.
7
Table 10.2:
An Example of a Time
0 ZeroCoupon Bond Price Curve
P(0,4) = .923845
P(0,3) = .942322
P(0,2) = .961169
P(0,1) = .980392
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 8
Table 10.3:
An Example of the Cash
Flows to a Coupon Bond
0
1
2
3
4
$5
$5
$100
time
coupon
principal
9
EXAMPLE: COUPON BOND CALCULATION
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/09/2008 for the course NBA 5550 taught by Professor Jarrow,robert during the Fall '08 term at Cornell University (Engineering School).
 Fall '08
 JARROW,ROBERT

Click to edit the document details