4.1. (a) Let the continuously compounded rate be
r
. Then we must have
e
r
°
0
:
25
=
1 + 0
:
14
=
4
;
r
=
0
:
1376
:
(b) Let the annually compounded rate be
r
. Then we must have
1 +
r
=
(1 + 0
:
14
=
4)
4
;
r
=
0
:
1475
:
4.3. The bond price is related to its yield via the following:
p
=
4
1 + 0
:
104
=
2
+
4
(1 + 0
:
104
=
2)
2
+
104
(1 + 0
:
104
=
2)
3
=
96
:
744
:
Now let°s use the zero rates to price the bond. Assuming that the zero rate
at 18 months is
R
per annum with semiannual compounding, we must have
96
:
744 =
4
1 + 0
:
10
=
2
+
4
(1 + 0
:
10
=
2)
2
+
104
(1 +
R=
2)
3
The solutions is
R
= 0
:
1042
:
4.5. The forward rate for the second quarter (between end of ±rst and end
of second quarters) is:
f
(2) =
8
:
2
°
2
±
8
:
0
°
1
2
±
1
= 8
:
4%
:
The rest of the forward rates are: 8.8%, 8.8%, 9.0%, and 9.2%.
4.6. Using continuously compounded zero rates and forward rates, the value
of the FRA is:
1000000
°
°
0
:
25
°
0
:
095
±
°
e
0
:
09
°
3
12
±
1
±±
°
e
±
0
:
086
°
15
12
= 893
:
56
:
Note that the 9.5% is quoted with quarterly compounding, but the forward
rate of 9% (between 4th and 5th quarter) is continuously compounded. There
fore
°
e
0
:
09
°
3
12
±
1
±
allows us to convert the continuously compounded forward
rate into a forward interest rate that would apply to a onequarter period. The
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 Spring '08
 Yu
 18 months, 10 months, 15month, 1 12.4%

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