Question

We want to price options using the binomial lattice. The current stock price is 104 and the strike price is 100. 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=0.02. Assume that the lenth of a period is one month.

1. Construct a binomial lattice that gives the price of a 5-month European call option.

2. Construct a binomial lattice that gives the price of a 5-month American put option.

Answer 1

Given data ,

Spot price = 104 and risk-free rate is r=0.02 =2%

strike price = 100.

Time = 5 months = 5/12 years

for binomial model , length of node(dt) = 1 month i.e 5 nodes in the model.

Answer 1)

for European Call option
At each node:
Upper value = Underlying Asset Price
Lower value = Option Price
Values in red are a result of early exercise.
Strike price = 100
Discount factor per step = 0.99
Time step, dt = 0.0833 years, 30.42 days
Growth factor per step, a = 1.0017
Probability of up move, p = 0.4
Up step size, u = 1.2
Down step size, d = 0.8

Answer2)

At each node:
Upper value = Underlying Asset Price
Lower value = Option Price
Values in red are a result of early exercise.
Strike price = 100
Discount factor per step = 0.99
Time step, dt = 0.0833 years, 30.42 days
Growth factor per step, a = 1.0017
Probability of up move, p = 0.4
Up step size, u = 1.2
Down step size, d = 0.8