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 : If the initial price S0 of the stock is $4 per share. and the interest rate is r = 10%, nd the appropriate price (at time 0) for a European-style option, expiring at time t = 2, whose payout is abs(S2 -4). (That is, the payout is always non-negative, and is the dierence between the time-2 value and the original value of the stock.)