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Option Payoffs
Problems 1 through 10: Assume that the stock is currently trading at $20 per share and options and bonds have the
prices given in the table below. Depending on the strike price (
X
) of the option or the face value (
FV
) of the bond, do
the following:
a)
Sketch the payoff and profit diagrams for the strategy.
b)
Describe the profitable range in terms of the price of the underlying security.
c)
Describe the maximum potential profits and losses.
X
or
FV
Call Premium
Put Premium
Bond Price
$
5
$
15.60
$
0.10
$
4.50
10
11.80
0.90
9.00
15
9.00
2.60
13.60
20
6.90
5.00
18.10
25
5.40
8.00
22.60
30
4.30
11.40
27.10
35
3.40
15.10
31.70
1.
Short one call,
X
=10; Long one bond,
FV
=10.
2.
Long one call,
X
=20; Short one call,
X
=30.
3.
Long one share of stock; short one call,
X
=20.
4.
Long one put,
X
=15; Long one call,
X
=25.
5.
Short one put,
X
=15; Long one call,
X
=20.
6.
Long one put,
X
=10; Short one put,
X
=20; Long one call,
X
=30.
7.
Short one put,
X
=10; Long one put,
X
=20; Short one call,
X
=20.
8.
Long two calls,
X
=25; Short one call,
X
=10; Long one bond,
FV
=10.
9.
Long one put,
X
=10; Short one put,
X
=15; Short one call,
X
=25; Long one call,
X
=30.
10. Short one share of stock; Short one put,
X
=20; Long one bond,
FV
=25; Long one call,
X
=25.
Problems 11 through 16: Describe (as I have in 110) the strategy depicted by each payoff diagram.
S
Payoff
+10
0
10
+10
+20
+20
S
Payoff
+10
0
10
+10
+20
+20
S
Payoff
+10
0
10
+10
+20
+20
S
Payoff
+10
0
10
+10
+20
+20
S
Payoff
+10
0
10
+10
+20
+20
S
Payoff
+10
0
10
+10
+20
+20
#11
#12
#13
#14
#15
#16
1
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View Full DocumentArbitrage
17. Suppose that there are two call options written on the same underlying asset. Call A has a strike price of
$50 and Call B has a strike price of $60. Call A’s premium is $5.25 and Call B’s premium is $6.50.
Describe the arbitrage opportunity that takes advantage of these prices and prove that this is an arbitrage
strategy.
Hint
: draw the payoff diagrams.
18. Suppose that there are two put options written on the same underlying asset. Put Y has a strike price of $30
and Put Z has a strike price of $40. Put Y’s premium is $3.25 and Put Z’s premium is $2.50. Describe the
arbitrage opportunity that takes advantage of these prices and prove that this is an arbitrage strategy.
Hint
: draw the payoff diagrams.
19. Suppose that you know that strike price X2 is greater than strike price X1 (i.e., X1 < X2). Generalizing the
results from problems 17 and 18, what conditions must hold in equilibrium for the call option premiums in
terms of X1 and X2 (assuming the same underlying asset and time to expiration)? That is, which call option
should have the higher premium? What about the put option premiums?
20. Suppose that a stock’s current price is $88 and the riskfree interest rate is 10%. Oneyear European call
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This note was uploaded on 05/20/2011 for the course ECON 5128 taught by Professor Ram during the Spring '11 term at Cambridge College.
 Spring '11
 Ram

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