This document discusses options and futures markets and provides solutions to example problems calculating call and put option values using one-step and two-step binomial trees. In question 1, the values of call and put options are calculated for two cases where the underlying stock price can move up or down by 10% or 20%. Question 2 extends this to a two-step binomial tree, and question 3 recalculates the options assuming they are American style. Finally, question 4 values call and put options where the strike price is 105 rather than 100 as in previous questions.

1. Options and Futures Markets
Class #10
4.6.2015
Prof Rafi Eldor
Mr. Eitan Zeevi

3. Question #1
One Step binomial tree
Calculate 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

4. 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
147
051
10
9011
90051
.
...
..








C 382
051
1
10
4
1
0
4
3
.
.






P
50
10020
10
.
.







h
Question #1 – Solution

5. 911
051
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
147
051
20
8021
05121
.
...
..








P
Question #1 – Solution

6. 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=1.1
Compare the values from question #1 to question #2, how
does the hedge ration change?

7. 15
051
1
21
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
0Cd
950
11020
21
.
.







hu 0hd
750
10020
15
.
.
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



h
7110
051
1
15
4
3
.
.






C
Summary – Call Option

8. Summary – Put Option
230
051
1
4
1
.
.






Pu
u= 1.10
d= 0.90
X= 100
r= 5%
0450
11020
1
.
.







hu 1
9020
18



.
hd 250
10020
5
.
.







h
41
051
1
4
23803
4
235
.
.
..





 
P
S= 121
110
100 99
90
81
P= 0
0.24
1.42 1
5.24
19
235
051
1
4
19
4
3
.
.






Pd

9. Question #3
Calculate again the options from question #2 but
this time assume they are American style options.

10. Summary – American option
230
051
1
4
1
.
.






Pu
u= 1.10
d= 0.90
X= 100
r= 5%
0450
11020
1
.
.







hu 1
9020
18



.
hd 490
10020
24010
.
.
.








h
552
051
1
4
23803
4
10
.
.
.





 
P
10Pd
S= 121
110
100 99
90
81
P= 0
0.24
2.55 1
10.00
19

11. Question #4
Calculate the value of Call option and Put option with
strike = 105
r=5%, d=0.9 and u=1.1
Compare the results from this question to question #1
Compare the values of the Call option to the Put option

12. Summary – Question #4
573
051
1
5
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
573
051
1
15
20
050
.
..
.






P

13. Thank You!