options and futures market - binomial exercise
TRANSCRIPT
Options and Futures Markets
Class #10
4.6.2015
Prof Rafi Eldor
Mr. Eitan Zeevi
Question #1
One Step binomial treeCalculate the value of a Call Option and Put Option with strike price = 100, under the following assumptions:
Stock = 100, r= 5%, uS = 110, dS= 90 Stock = 100, r= 5%, uS = 120, dS= 80
Case A
u= 1.10 S=
d= 0.90 110
X= 100
r= 5% 100
90
C= P=
10 0
7.14 2.38
0 10
147051
10
9011
90051.
...
..
C 382
051
110
4
10
4
3.
.
P
5010020
10.
.
h
Question #1 – Solution
911051
20
8021
80051.
...
..
C
Case B
u= 1.20 S=
d= 0.80 120
X= 100
r= 5% 100
80
C= P=
20 0
11.90 7.14
0 20
147051
20
8021
05121.
...
..
P
Question #1 – Solution
Question #2 – Two Steps
Two steps binomial tree:Calculate the value of a Call option and Put option with strike price = 100, r=5%,Each step d=0.9 and u=1.1Compare the values from question #1 to question #2, how does the hedge ration change?
15051
121
4
3
.Cu
u= 1.10
d= 0.90
X= 100
r= 5%
S= 121
110
100 99
90
81
C= 21
15.00
10.71 0
-
0
0Cd
95011020
21.
.
hu 0hd
75010020
15.
.
h
7110051
115
4
3.
.
C
Summary – Call Option
Summary – Put Option
230051
1
4
1.
.
Pu
u= 1.10
d= 0.90
X= 100
r= 5%
045011020
1.
.
hu 1
9020
18
.hd 250
10020
5.
.
h
41051
1
4
23803
4
235.
.
..
P
S= 121
110
100 99
90
81
P= 0
0.24
1.42 1
5.24
19
235051
1
4
19
4
3.
.
Pd
Question #3
Calculate again the options from question #2 but this time assume they are American style options.
Summary – American option
230051
1
4
1.
.
Pu
u= 1.10
d= 0.90
X= 100
r= 5%
045011020
1.
.
hu 1
9020
18
.hd 490
10020
24010.
.
.
h
552051
1
4
23803
4
10.
.
.
P
10Pd
S= 121
110
100 99
90
81
P= 0
0.24
2.55 1
10.00
19
Question #4
Calculate the value of Call option and Put option with strike = 105r=5%, d=0.9 and u=1.1
Compare the results from this question to question #1Compare the values of the Call option to the Put option
Summary – Question #4
573051
15
20
150.
..
.
C
u= 1.10 S=
d= 0.90 110
X= 105
r= 5% 100
90
C= P=
5 0
3.57 3.57
0 15
573051
115
20
050.
..
.
P
Thank You!