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SOLUTIONS, STUDY PROBLEM SET 6 (BKM, 8
TH
ED)
Chapter 20
10.
a.
Position
S
T
< X
1
X
1
≤
S
T
≤
X
2
X
2
< S
T
≤
X
3
X
3
< S
T
Long call (X
1
)
0
S
T
– X
1
S
T
– X
1
S
T
– X
1
Short 2 calls (X
2
)
0
0
–2(S
T
– X
2
)
–2(S
T
– X
2
)
Long call (X
3
)
0
0
0
S
T
– X
3
Total
0
S
T
– X
1
2X
2
– X
1
– S
T
(X
2
–X
1
) – (X
3
–X
2
) = 0
X
2
– X
1
S
T
X
1
X
2
Payoff
X
3
b.
Position
S
T
< X
1
X
1
≤
S
T
≤
X
2
X
2
< S
T
Buy call (X
2
)
0
0
S
T
– X
2
Buy put (X
1
)
X
1
– S
T
0
0
Total
X
1
– S
T
0
S
T
– X
2
X
1
S
T
X
1
X
2
Payoff
1
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View Full Document12.
a.By writing covered call options, Jones receives premium income of $30,000. If, in
January, the price of the stock is less than or equal to $45, then Jones will have his
stock plus the premium income. But the
most
he can have at that time is ($450,000 +
$30,000) because the stock will be called away from him if the stock price exceeds
$45. (We are ignoring here any interest earned over this short period of time on the
premium income received from writing the option.) The payoff structure is:
Stock price
Portfolio value
less than $45
10,000 times stock price + $30,000
greater than $45
$450,000 + $30,000 = $480,000
This strategy offers some extra premium income but leaves Jones subject to
substantial downside risk. At an extreme, if the stock price fell to zero, Jones would
be left with only $30,000. This strategy also puts a cap on the final value at $480,000,
but this is more than sufficient to purchase the house.
b.
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 Spring '09
 TongYao
 Management

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