550.445 Modeling and Analysis of Securities and Financial Markets II, Spring 2010
TA Section 03
Peter C.L. Lin
[email protected]
1
Homework Review
29.11
To calculate the convexity adjustment for the fiveyear rate define the price of a five year bond, as a function of its yield as
G
(
y
)
=
e

5
y
G
prime
(
y
)
=

5
e

5
y
G
primeprime
(
y
)
=
25
e

5
y
.
The convexity adjustment is
0
.
5
×
0
.
08
2
×
0
.
25
2
×
4
=
0
.
004
.
Similarly for the two year rate the convexity adjustment is
0
.
5
×
0
.
08
2
×
0
.
25
2
×
4
×
2
=
0
.
0016
.
We can therefore value the derivative by assuming that the five year rate is 8
.
4% and the twoyear rate is 8
.
16%. The value of
the derivative is
0
.
24
e

0
.
08
×
4
=
0
.
174
.
If the payo
ff
occurs in five years rather than four years it is necessary to make a timing adjustment. From equation (29.4) this
involves multiplying the forward rate by
exp
parenleftBigg

1
×
0
.
25
×
0
.
25
×
0
.
08
×
4
×
1
1
.
08
parenrightBigg
=
0
.
98165
.
The value of the derivative is
0
.
24
×
0
.
98165
e

0
.
08
×
5
=
0
.
158
.
2
Siegel’s Exchange Rate Paradox (cont.)
Last time, we showed that
1
Q
has mean rate of change
R
f
(
t
)

R
(
t
)
+
σ
2
2
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 Spring '10
 Jooe
 Derivative, Probability theory, convexity adjustment, domestic riskneutral measure

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