Math 489/889
Stochastic Processes and
Advanced Mathematical Finance
Final Exam Solutions
Steve Dunbar
Thursday, December 17, 2009
Initializations
(1.1)
(1.2)
_R
(1.3)
Problem 1
A stock has a constant volatility of 18% and the risk-free
interest rate (compounded continuously) is 6%. What is the value
of an option to buy the stock for $25 in two years time, given the
current stock price is $20?
20
25
0.06
0.18
2
(2.1)
20
25
0.06
0.18
2
(2.2)
1.220977956
(2.3)
(2.4)
(2.5)
(2.6)
0.390541907415555667
(2.7)
0.297201864689145112
(2.8)
1.220977957
(2.9)
50
40
30
20
10
0
10
20
30
x
40
50
Problem 3
(3.1)
(3.2)
(3.3)
0.2
(3.4)
Spreadsheet(1)
A
B
C
D
E
F
G
H
1
2
3
4
5
6
7
8
9
10
11
Problem 5
2
2.82
(4.1)
(4.2)
0.2725894983
(4.3)
0.3605126178
(4.4)
0.4075596985
(4.5)