Answer:
Explanation:
The Risk neutral probability is given by
e
rt
−
D / U-D
U=1.1
D=0.9
R=0.12
T=3/12
π
u
=
e∧
0.12
∗
3
/
12
−
0.9
/1.1
−
0.9
=0.652
π
d
=
1−
0.652
=
0.348
The values of american and european options at each node is given in the following table.
0.652
0
0.81 48.4
0.652
0.81
American option value 2.54 44
probability 0.652/0.3478'
Option value 2.12 2.4
Futures price 40 6 39.6
0.3478
4.76
36
0.3478
9.6
32.4
Time period 0 3 6
the value at up node at 3 months is given by = (
0.652∗
0
)
+
(
0.3478
∗
2.4
)/e
∧0.12
∗
3
/
12 = 0.81
Hence, value of european put option =$2.12
Value of American put option = 2.54