STAT 473
HW 1 Solution
1.
Recall
Since both options are atthe money,
.
We have
Therefore, in order to be consistent with Call Put Formula,
We must have
2.
Therefore, there is an arbitrage opportunity.
Buy Low Sell High:
Long RHS & Short LHS:
The profit after one year = $ 1.3952
C K
,
T
(
)
−
P K
,
T
(
)
=
S
0
−
K
⋅
e
−
rT
K
=
S
0
C K
,
T
(
)
−
P K
,
T
(
)
=
S
0
−
S
0
⋅
e
−
rT
=
S
0
⋅
1
−
e
−
rT
(
)
∀
T
>
0,
−
r
⋅
T
<
0
e
−
r
⋅
T
<
1
RHS
=
S
0
⋅
1
−
e
−
rT
(
)
>
0
C K
,
T
(
)
>
P K
,
T
(
)
C K
,
T
(
)
−
P K
,
T
(
)
=
S
0
⋅
e
−
δ
T
−
K
⋅
e
−
rT
LHS
=
2.34
−
8.00
=
−
5.66
RHS
=
40
×
e
−
2%
×
1
−
50
×
e
−
8%
×
1
≈ −
6.95
LHS
>
RHS
Transaction @ t = 0
Cash Flow @ t = 0
If S(T) > K
If S(T) < K
Long Stock
40 e^(0.02) = 39.2079
S(T)
S(T)
Short Call
+ 2.34
 [S(T)  K]
Not Exercised: 0
Long Put
 8.00
Not Exercised: 0
K  S(T)
Short Treasury
50 e^(0.08) = 46.1558
 K
 K
Lend Money
1.2879
1.2879 e^(0.08) =
1.3952
1.2879 e^(0.08) =
1.3952
TOTAL
0
$ 1.3952
$ 1.3952
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of
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STAT 473
HW 1 Solution
3.
Notice that the second dividend is 9 months from today,
but the agreement period is only 6 months.
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 Spring '08
 Staff
 treasury bills, Long Stock

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