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550.446 Risk Management Analysis and Hedging, Spring 2010
TA Section 02
Peter C.L. Lin
peter.lin@jhu.edu
1
Homework Review
4.16
The investors overall return is
1
.
08
×
0
.
92
×
1
.
12
×
0
.
88

1
=

0
.
0207
or

2
.
07% for the four years.
6.16
The price, delta, gamma, vega, theta, and rho of the option are 3
.
7008, 0
.
6274, 0
.
05, 0
.
1135,

0
.
00596, and 0
.
1512. When the
stock price increases to 30
.
1, the option price increases to 3
.
7638. The change in the option price is 3
.
7638

3
.
7008
=
0
.
063.
Delta predicts a change in the option price of 0
.
6274
×
0
.
1
=
0
.
0627 which is very close. When the stock price increases to
30
.
1, delta increases to 0
.
6324. The size of the increase in delta is 0
.
6324

0
.
6274
=
0
.
005. Gamma predicts an increase of
0
.
05
×
0
.
1
=
0
.
005 which is (to three decimal places) the same. When the volatility increases from 25% to 26%, the option
price increases by 0
.
1136 from 3
.
7008 to 3
.
8144. This is consistent with the vega value of 0
.
1135. When the time to maturity
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 Spring '10
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