Our stock currently costs $4 per share. In each time period, the value of the stock will either increase or decrease by 50%, and the risk-free interest rate is 10%. Let S0, S1, and S2 be the prices of Stock X at times 0, 1, and 2, and suppose we are selling a European-style security expiring at time 2, whose payoot at expiration is (S2-(S1S2)^(1/2))+
(a) Find the risk-neutral price of this option at time 0.
(b) Describe the hedging process for this option in the case that the first movement of the stock is upwards (that is, assuming the first coin-°ip lands on Heads). That is, at times 0 and 1, find the value of a portfolio which replicates this security, compute the number of shares of stock we buy or short-sell, and find the amount of money we invest or borrow at the risk-free rate. Show that in each case, the portfolio replicates the security