Consider a binomial world in which the current stock price of 80 can either go up by 10% or down by 7%. The risk free rate is 5%. Assume a one-period world. Use the binomial tree below and answer questions about a call with an exercise price of 82.

Calculate the stock price in each state at time 1.

Calculate the call's value in each state at time 1.

Calculate the hedge ratio and at time 0.

Calculate the call's value at time 0.

Suppose at time 0 you try to construct a risk-free portfolio. You want to include 20,000 short calls in the portfolio; then how many underlying stocks should be included?