Suppose that instead of our usual pricing scenario, we have a stock whose price will become either its square or its square root at the end of each period; that is, for k >=0,
Sk+1 = (Sk)^2 if Wk+1 = H
Sk+1 = sqrt(Sk) if wk+1 = T
where the initial price S0 of the stock is $4 per share. Find an appropriate price (at time 0) for a European-style option, expiring at time 2, whose payout is absolute value of (S2-4). Assume the risk-free interest rate r is 10%.