1
CHAPTER 21
Valuing Options
Answers to Problem Sets
1.
a.
Using riskneutral method, (
p
X 20) + (1 
p
)(16.7) = 1,
p
= .48.
Value of call =
( ) ( )
8
.
3
01
.
1
0
52
.
8
48
.
=
×
+
×
b
.
Delta =
=
544
.
7
.
14
8
=
c.
d.
Possible stock prices with call option prices in parentheses:
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e.
Delta =
=
544
.
7
.
14
8
=
2.
(a) No. The maximum delta is 1.0 when the ratio of stock price to exercise
price is very high. (b) No. (c) Delta increases. (d) Delta increases.
3.
Using the replicatingportfolio method:
a.
If month 3 stock price = 350.85, delta = (30 – 0)/(430286.27) =
.209
To replicate call, buy .209 shares, and borrow PV(59.752)
Option value = .209 X 350.85 – 59.752/1.0075 = 13.93
b.
If month 3 stock price = 527, delta = (245.90 – 30)/(645.90 – 430) =
1
To replicate call, buy 1 share, and borrow PV(527)
Option value = 1 X 527 – 400/1.0075 = 129.98
c.
At month 0 delta = (129.98 – 13.93)/(527 – 350.85) = .659
To replicate call, buy .659 shares, and borrow PV(217.29)
Option value = .659 X 430 – 217.29/1.0075 = 67.7
Using the riskneutral method:
p X .2269 + (1 – p) X .184 = 0.0075: p = .4671
a.
If month 3 stock price = 350.85
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 Spring '11
 Wilson

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