We want to price options using the binomial lattice. The current stock price is
ID: 3438151 • Letter: W
Question
We want to price options using the binomial lattice. The current stock price is 54 and the strike price is 50. Assume that the stock up-trend rate is u = 1.2 with probability p = 0.4 and the down-trend rate is d = 0.8 with probability 1 p = 0.6. The annual risk-free rate is r = 0.005. Assume that the length of a period is one month.
1. Construct a binomial lattice that show the evolution of the stock price during the 5 months.
2. Construct a binomial lattice that gives the price of a 5-month European call option.
3. Construct a binomial lattice that gives the price of a 5-month American put option.
Explanation / Answer
Stock Price
54
0
1
2
3
4
5
pay off
Strike
50
u
1.2
134.364
0
d
0.8
111.972
p
0.4
93.312
89.576
0
r
0.005
77.76
74.648
64.8
62.208
59.72
0
Stock Price
54
51.84
49.768
43.2
41.472
39.816
14.184
34.56
33.176
27.648
26.544
27.456
19.72
15.776
38.224
American Put:
Let Vs,t be the option value when stock price is s at time t.
Vs,t = (p*s*u+(1-p)*s*d)*exp(-r*t)
t = 1/5 = 0.2
0
0
0
0
30.4821
0
73.09854
50.88491
0
option price
118.4966
101.705
8.494398
149.0782
135.8558
14.18
181.058
22.11259
211.6767
27.46
33.86178
38.22
Stock Price
54
0
1
2
3
4
5
pay off
Strike
50
u
1.2
134.364
0
d
0.8
111.972
p
0.4
93.312
89.576
0
r
0.005
77.76
74.648
64.8
62.208
59.72
0
Stock Price
54
51.84
49.768
43.2
41.472
39.816
14.184
34.56
33.176
27.648
26.544
27.456
19.72
15.776
38.224
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