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Oduvanchick [21]
2 years ago
4

10.12 Let S = $100, K = $95, r = 8% (continuously compounded), σ = 30%, δ = 0, T = 1 year, and n = 3. a. Verify that the binomia

l 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.
Business
1 answer:
Ivenika [448]2 years ago
6 0

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

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