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1
#1 (a):
•
Buy call at
K
= 10
•
Sell call at
K
= 15
•
Buy call at
K
= 18
•
Sell 3 calls at
K
= 23
•
Buy 2 calls at
K
= 28
#1 (b):
•
We lose
C
(10) = 2 buying a call at
K
= 10
•
We gain
C
(15) = 2
.
5 writing a call at
K
= 15
•
We lose
C
(18) = 2
.
8 buying a call at
K
= 18
•
We gain 3
C
(23) = 9
.
9 writing 3 calls at
K
= 23
•
we lose 2
C
(28) = 7
.
6 buying 2 calls at
K
= 28
The net of this is 0, so the premium paid at time 0 to establish the above position at time 1
is 0. As a result, shift the payoﬀ graph up buy 0
×
(1
.
05) to get the proﬁt graph, i.e. the payoﬀ
graph is the proﬁt graph.
#2:
We can establish a synthetic forward with a lockedin price of 12
,
200 at time 1 by buying a
call with strike price 12
,
200 and writing a put with strike price 12
,
200 (see
putcall parity
in the
notes and
synthetic forward
in the Derivatives Markets text). Let
C
be the price of the call and
P
be the price of the put. Then
C

P
is the total premium we pay at time 0 to establish the forward.
By putcall parity,
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 Fall '09

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