We want to price options using the binomial lattice The curr

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.

Solution

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