Construct a 2 step binomial tree to price a one-week option. The tree assumes that the current stock price is 100, the stock return volatility is 25%, and the risk-free interest rate is zero

Q1:

a.What is the time interval, t, between steps?

b.What is the maximum stock price on the tree?

c.Suppose the current stock price was 101 instead of 100. How much does the maximum stock price change?

d.Use the binomial tree to price a call of strike 104.

Q2: What is the option implied probability that a call of strike 104 will expire in the money?

Q3: What is your estimate of the delta of the call of strike 104?

(Recall that the delta is the sensitivity of the option price to changes in the underlying stock price).

***Formula:

T = time to maturity in years

N = number of steps in the binomial tree

t = time between each step in the binomial tree

= T/N

u = exp(volatility x sqrt(t))

d = 1/u

R = exp(r t)

q = (R-d)/(u-d)

Note:exp(r t) = e^{r x t}