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Assignment 3 Solutions
Question 1.
Putcall parity gives
0
S
p
Ke
D
c
rT
+
=
+
+
−
29
30
5
.
0
5
.
0
2
12
/
6
%*
10
12
/
5
%*
10
12
/
2
%*
10
+
=
+
+
+
−
−
−
p
e
e
e
p=2.51
The price of this put option should be $2.51.
Question 2.
The present value of all dividends:
D=0.5e
10%*2/12
+0.5*e
10%*5/12
=0.9713
Since
c+D+Xe
rT
=p+S
0
p=C+D+ Xe
rT
S
0
=2+0.9713+30* e
10%*6/12
29=2.5082
If the put option is traded at $3, there is an arbitrage opportunity.
±
Short a put option at $3 and a share of stock at $29
±
Long a call option at $2 and invest 0.9713+30 e
10%*6/12
into the market
money account with an interest rate of 10%.
The rest (29+320.971330 e
10%*6/12
=0.4918) is your arbitrage profit.
At the end of 2
nd
month, withdraw $0.5 to pay the dividend.
At the end of 5
th
month, withdraw $0.5 to pay the dividend.
At the maturity (the 6
th
month), hold a long position of a call, a short position of a put and
a short positon of a share of stock.Withdraw an amount of $30.
If the stock price is greater than $30, the call will be exercised and pay $30 to buy the
share.
If the stock price is smaller than $30, the put will be exercised and pay $30 to buy back
the share.
If the stock price is equal to $30, no option will be exercised. Buy back the share with the
$30.
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View Full DocumentQuestion 3.
Choose one portfolio: A (long call options with strike prices K1 and K3, short two
options with strike price K2)
If
, all options with strike prices K1, K2 will be exercised, A value:
3
K
S
T
≥
0
2
3
1
2
=
−
−
K
K
K
If
, options with strike prices K1, K2 will be exercised, A value:
2
3
K
S
K
T
≥
>
0
2
1
2
>
−
−
T
S
K
K
If
, just option with strike price K1 will be exercised, the value of A:
1
2
K
S
K
T
≥
>
0
1
>
−
K
S
T
If
, all the options will not be exercised, the value of A: =0
1
K
S
T
<
The value of A is always nonnegative, so the price of portfolio A should also be non
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 Winter '09
 Adam
 Dividends

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