Answer:
American Put Value
N. down moves 3 2 1 0
0 0 0 1.09077967 6.677901
1 0 2.0623567169 11.7087201
2 3.8993348796 20.4035172625
3 30.5715733249
Explanation:
Let S = $100, K = $95, r = 8% (continuously compounded), σ = 30%, δ = 0, T = 1 year, and n = 3. a. Verify that the binomial option price for an American call option is $18.283. Verify that there is never early exercise; hence, a European call would have the same price. b. Show that the binomial option price for a European put option is $5.979. Verify that put-call parity is satisfied. c. Verify that the price of an American put is $6.678.
Let S0= $100, K= $95, r= 8% (continuously compounded), σ= 30%, δ= 0, T= 1 year, and n= 3.
a. Confirm that the binomial option price for an American call option is$18.283. Hint: there is no early exercise; therefore, a European call would have the same price.
S0 100
K 95
σ 0.3
δ 0
u 1.2212461202
d 0.8636925537
r 0.08
T 1
n 3
h 0.3333333333
p* 0.4568066592
American Call Value
N. down moves 3 2 1 0
0 87.1417860953 56.6440624107 33.1493175 18.28255
1 33.8147423997 15.0403285537 6.6897296
2 0 0
3 0
European Call Value
N. down moves 3 2 1 0
0 87.1417860953 56.6440624107 33.1493175 18.28255
1 33.8147423997 15.0403285537 6.6897296
2 0 0
3 0
The American option is never exercised early, and the American and European values are the s.
b. Demonstrate that the binomial option price for a European put option is 5.979%. Verify that put-call parity is satisfied.
European Put Value
N. down moves 3 2 1 0
0 0 0 1.09077967 5.978605
1 0 2.0623567169 10.3865484
2 3.8993348796 17.903663451
3 30.5715733249
Put call parity:
C - P: 12.3039470933
S-Ke^(-(r-5)T) 12.3039470933
c. Confirm that the price of an American put is $6.678
American Put Value
N. down moves 3 2 1 0
0 0 0 1.09077967 6.677901
1 0 2.0623567169 11.7087201
2 3.8993348796 20.4035172625
3 30.5715733249
