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Cornell University
Fall 2010
Economics 3330: Problem Set 10 Solutions
1. Consider the following parameters: current stock price $50, standard deviation 50%, exercise
price $50, interest rate 4%.
a. Use the BlackScholes formula to find the value of a call option with an exercise price of $50
and expiration of 1 year.
d
1
= 0.33
N(d
1
) = .63
d
2
= –0.17
N(d
2
) = .43
Xe
–rT
= $52.05
C = S
0
N(d1)  Xe
–rT
N(d2) = $10.68
b. Use the BlackScholes formula to find the value of a put option with an exercise price of $50
and expiration of 6 months.
P= 8.73
c. Verify putcall parity.
P = C – S
0
+ PV(X) = $10.68 – $50 + $48.07 = $8.73
2. Find how the value of the call option from problem one changes when each of the following
changes in parameters is made
individually
.
In other words, for each of the following, you are
only changing
one
parameter relative to problem
one
.
a. Time to expiration 3 months. C falls to 5.20
b. Standard deviation 25%. C falls to 5.92
c. Exercise price $55. C falls to 8.79
d. Interest rate 10%. C rises to 9.96
3. Option deltas
a.What is the delta of a call option?
How is it approximated in the BlackScholes model?
b.Fill in the following table for a call option with exercise stock price 50, standard deviation 50%,
interest rate 4%, and expiration in one year. Sketch the resulting graph.
10
20
30
40
45
50
55
60
70
80
90
100
140
Price
0
.24
1.73 5.23 7.74
10.68 14.01 17.65 25.68 34.40 43.57
53.03 92.19
Delta
0
.07
.24
.45
.55
.63
.52
.69
.84
.90
.93
.96
.99
c. Now do the same for a put option, including sketching the resulting graph.
4. A hedge fund has a net asset value of $100 per share and a high water mark of $110.
The
standard deviation of the fund’s annual returns is 40% and the riskfree rate is 2%.
The incentive
fee is 20%.
All answers should be given in terms of one year.
a. According to BlackScholes, what is the value of the incentive fee?
First, compute the BlackScholes value of a call option with the following parameters:
S
0
= 100
X = 110
R = 0.02
= 0.4 T = 1 year
Therefore: C = $12.84. The value of the annual incentive fee is: 0.20 × C = 0.20 × $12.84 = $2.57
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View Full Documentb. What would the incentive fee be worth if the fund had no high water mark?
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 Fall '08
 MBIEKOP
 Economics

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