A non-dividend paying stock, currently priced at 140, is expected to go up by 10% or go down by 10% over a period. The risk-free rate for one period is 4%.

a) Build a 2-period tree of stock prices.

b) Price a call option with a strike of $120 using the binomial pricing model.

c) Calculate and explain the hedge ratio that makes risk-neutral pricing possible. Demonstrate the value of the hedge portfolio for shorting 1000 call options currently (at the beginning of the tree) and both when the stock price goes up and goes down (once).

d) How does the hedge ratio change and how many shares do you need to buy/sell to stay hedged in point u?